SwePub - sökning: WFRF:(Kleinschmidt Axel)

Numrering	Referens	Omslagsbild	Hitta
1.	Ahlén, Olof, et al. (författare) Fourier coefficients attached to small automorphic representations of SLn (A) 2018 Ingår i: Journal of Number Theory. - : Elsevier BV. - 0022-314X .- 1096-1658. ; 192, s. 80-142 Tidskriftsartikel (refereegranskat)abstract We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of SLn(A) are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit formula for the Fourier expansion, analogously to the Piatetski-Shapiro–Shalika formula. In addition, we derive expressions for Fourier coefficients associated to all maximal parabolic subgroups. These results have potential applications for scattering amplitudes in string theory.
2.	Bao, Ling, 1980, et al. (författare) Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons 2013 Ingår i: Journal of Physics: Conference Series. - : IOP Publishing. - 1742-6588 .- 1742-6596. ; 462:1 Konferensbidrag (refereegranskat)abstract Type IIA string theory compactified on a rigid Calabi-Yau threefold gives rise to a classical moduli space that carries an isometric action of U(2, 1). Various quantum corrections break this continuous isometry to a discrete subgroup. Focussing on the case where the intermediate Jacobian of the Calabi-Yau admits complex multiplication by the ring of quadratic imaginary integers script O signd, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2, 1; script O signd). Based on this proposal we construct an Eisenstein series invariant under this duality group and study its non-Abelian Fourier expansion. This allows the prediction of non-perturbative effects, notably the contribution of D2- and NS5-brane instantons. The present work extends our previous analysis in 0909.4299 which was restricted to the special case of the Gaussian integers script O sign1 = ℤ[i].
3.	Bergshoeff, E. A., et al. (författare) E10 and gauged maximal supergravity 2009 Ingår i: Journal of High Energy Physics. - : Springer Science and Business Media LLC. - 1029-8479 .- 1126-6708. ; 2009:1, s. 020 (artno)- Tidskriftsartikel (refereegranskat)abstract We compare the dynamics of maximal three-dimensional gauged supergravity in appropriate truncations with the equations of motion that follow from a one-dimensional E10/K(E-10) coset model at the first few levels. The constant embedding tensor, which describes gauge deformations and also constitutes an M-theoretic degree of freedom beyond eleven-dimensional supergravity, arises naturally as an integration constant of the geodesic model. In a detailed analysis, we find complete agreement at the lowest levels. At higher levels there appear mismatches, as in previous studies. We discuss the origin of these mismatches.
4.	Berman, David S., et al. (författare) The gauge structure of generalised diffeomorphisms 2013 Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 1301:1, s. 64- Tidskriftsartikel (refereegranskat)abstract We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show that the gauge algebra is infinitely reducible, i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised diffeomorphisms gives such a reducibility transformation. We give a concrete description of the ghost structure, and demonstrate that the infinite sums give the correct (regularised) number of degrees of freedom. The ghost towers belong to the sequences of rep- resentations previously observed appearing in tensor hierarchies and Borcherds algebras. All calculations rely on the section condition, which we reformulate as a linear condition on the cotangent directions. The analysis holds for n
5.	Bossard, Guillaume, et al. (författare) Beyond E11 2017 Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :5 Tidskriftsartikel (refereegranskat)abstract We study the non-linear realisation of E-11 originally proposed by West with particular emphasis on the issue of linearised gauge invariance. Our analysis shows even at low levels that the conjectured equations can only be invariant under local gauge transformations if a certain section condition that has appeared in a different context in the E-11 literature is satisfied. This section condition also generalises the one known from exceptional field theory. Even with the section condition, the E-11 duality equation for gravity is known to miss the trace component of the spin connection. We propose an extended scheme based on an infinite-dimensional Lie superalgebra, called the tensor hierarchy algebra, that incorporates the section condition and resolves the above issue. The tensor hierarchy algebra defines a generalised differential complex, which provides a systematic description of gauge invariance and Bianchi identities. It furthermore provides an E-11 representation for the field strengths, for which we define a twisted first order self-duality equation underlying the dynamics.
6.	Bossard, Guillaume, et al. (författare) Extended geometry of magical supergravities 2023 Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :5 Tidskriftsartikel (refereegranskat)abstract We provide, through the framework of extended geometry, a geometrisation of the duality symmetries appearing in magical supergravities. A new ingredient is the general formulation of extended geometry with structure group of non-split real form. A simple diagrammatic rule for solving the section constraint by inspection of the Satake diagram is derived.
7.	Bossard, Guillaume, et al. (författare) Generalised diffeomorphisms for E9 2017 Ingår i: Physical Review D - Particles, Fields, Gravitation and Cosmology. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 96, s. 106022- Tidskriftsartikel (refereegranskat)abstract We construct generalised diffeomorphisms for E9 exceptional field theory. The trans- formations, which like in the E8 case contain constrained local transformations, close when acting on fields. This is the first example of a generalised diffeomorphism alge- bra based on an infinite-dimensional Lie algebra and an infinite-dimensional coordi- nate module. As a byproduct, we give a simple generic expression for the invariant tensors used in any extended geometry. We perform a generalised Scherk–Schwarz reduction and verify that our transformations reproduce the structure of gauged supergravity in two dimensions. The results are valid also for other affine algebras.
8.	D'Hoker, Eric, et al. (författare) Elliptic modular graph forms. Part I. Identities and generating series 2021 Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :3 Tidskriftsartikel (refereegranskat)abstract Elliptic modular graph functions and forms (eMGFs) are defined for arbitrary graphs as natural generalizations of modular graph functions and forms obtained by including the character of an Abelian group in their Kronecker-Eisenstein series. The simplest examples of eMGFs are given by the Green function for a massless scalar field on the torus and the Zagier single-valued elliptic polylogarithms. More complicated eMGFs are produced by the non-separating degeneration of a higher genus surface to a genus one surface with punctures. eMGFs may equivalently be represented by multiple integrals over the torus of combinations of coefficients of the Kronecker-Eisenstein series, and may be assembled into generating series. These relations are exploited to derive holomorphic subgraph reduction formulas, as well as algebraic and differential identities between eMGFs and their generating series.
9.	Dorigoni, Daniele, et al. (författare) Modular graph forms from equivariant iterated Eisenstein integrals 2022 Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :12 Tidskriftsartikel (refereegranskat)abstract The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's alternative construction of non-holomorphic modular forms in the recent mathematics literature from so-called equivariant iterated Eisenstein integrals. In this work, we provide the first validations beyond depth one of Brown's conjecture that equivariant iterated Eisenstein integrals contain modular graph forms. Apart from a variety of examples at depth two and three, we spell out the systematics of the dictionary and make certain elements of Brown's construction fully explicit to all orders.
10.	Dorigoni, Daniele, et al. (författare) Poincare series for modular graph forms at depth two. Part I. Seeds and Laplace systems 2022 Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :1 Tidskriftsartikel (refereegranskat)abstract We derive new Poincare-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus one. The Poincare series are constructed from iterated integrals over single holomorphic Eisenstein series and their complex conjugates, decorated by suitable combinations of zeta values. We evaluate the Poincare sums over these iterated Eisenstein integrals of depth one and deduce new representations for all modular graph forms built from iterated Eisenstein integrals at depth two. In a companion paper, some of the Poincare sums over depth-one integrals going beyond modular graph forms will be described in terms of iterated integrals over holomorphic cusp forms and their L-values.
11.	Dorigoni, Daniele, et al. (författare) Poincare series for modular graph forms at depth two. Part II. Iterated integrals of cusp forms 2022 Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :1 Tidskriftsartikel (refereegranskat)abstract We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincare series in a companion paper. The source term of the Laplace equation is a product of (derivatives of) two non-holomorphic Eisenstein series whence the modular invariants are assigned depth two. These modular invariant functions can sometimes be expressed in terms of single-valued iterated integrals of holomorphic Eisenstein series as they appear in generating series of modular graph forms. We show that the set of iterated integrals of Eisenstein series has to be extended to include also iterated integrals of holomorphic cusp forms to find expressions for all modular invariant functions of depth two. The coefficients of these cusp forms are identified as ratios of their L-values inside and outside the critical strip.
12.	Fleig, Philipp, et al. (författare) Eisenstein series and automorphic representations 2015 Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the (rational) adeles A, thereby also paving the way for connections to number theory, representation theory and the Langlands program. Most of the results we present are already scattered throughout the mathematics literature but our exposition collects them together and is driven by examples. Many interesting aspects of these functions are hidden in their Fourier coefficients with respect to unipotent subgroups and a large part of our focus is to explain and derive general theorems on these Fourier expansions. Specifically, we give complete proofs of Langlands' constant term formula for Eisenstein series on adelic groups G(A) as well as the Casselman--Shalika formula for the p-adic spherical Whittaker vector associated to unramified automorphic representations of G(Q_p). Somewhat surprisingly, all these results have natural interpretations as encoding physical effects in string theory. We therefore introduce also some basic concepts of string theory, aimed toward mathematicians, emphasising the role of automorphic forms. In addition, we explain how the classical theory of Hecke operators fits into the modern theory of automorphic representations of adelic groups, thereby providing a connection with some key elements in the Langlands program, such as the Langlands dual group LG and automorphic L-functions. Our treatise concludes with a detailed list of interesting open questions and pointers to additional topics where automorphic forms occur in string theory.
13.	Fleig, Philipp, et al. (författare) Eisenstein series and automorphic representations 2018 Bok (övrigt vetenskapligt/konstnärligt)
14.	Fleig, Philipp, et al. (författare) Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors 2014 Ingår i: Communications in Number Theory and Physics. - 1931-4531 .- 1931-4523. ; 8:1, s. 41-100 Tidskriftsartikel (refereegranskat)abstract Motivated by string theory scattering amplitudes that are invariant under a discrete U-duality, we study Fourier coefficients of Eisenstein series on Kac-Moody groups. In particular, we analyse the Eisenstein series on E_9(R), E_10(R) and E_11(R) corresponding to certain degenerate principal series at the values s=3/2 and s=5/2 that were studied in 1204.3043. We show that these Eisenstein series have very simple Fourier coefficients as expected for their role as supersymmetric contributions to the higher derivative couplings R^4 and \partial^{4} R^4 coming from 1/2-BPS and 1/4-BPS instantons, respectively. This suggests that there exist minimal and next-to-minimal unipotent automorphic representations of the associated Kac-Moody groups to which these special Eisenstein series are attached. We also provide complete explicit expressions for degenerate Whittaker vectors of minimal Eisenstein series on E_6(R), E_7(R) and E_8(R) that have not appeared in the literature before.
15.	Gerken, Jan E., et al. (författare) All-order differential equations for one-loop closed-string integrals and modular graph forms 2020 Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :1 Tidskriftsartikel (refereegranskat)abstract We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories. These closed-string integrals are shown to obey homogeneous and linear differential equations in the modular parameter of the torus. We spell out the first-order Cauchy-Riemann and second-order Laplace equations for the generating functions for any number of external states. The low-energy expansion of such torus integrals introduces infinite families of non-holomorphic modular forms known as modular graph forms. Our results generate homogeneous first- and second-order differential equations for arbitrary such modular graph forms and can be viewed as a step towards all-order low-energy expansions of closed-string integrals.
16.	Gerken, Jan E., et al. (författare) Generating series of all modular graph forms from iterated Eisenstein integrals 2020 Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; 2020:7 Tidskriftsartikel (refereegranskat)abstract We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes. By analysing the differential equation of the generating series we construct a solution for their low-energy expansion to all orders in the inverse string tension alpha '. Our solution is expressed through initial data involving multiple zeta values and certain real-analytic functions of the modular parameter of the torus. These functions are built from real and imaginary parts of holomorphic iterated Eisenstein integrals and should be closely related to Brown's recent construction of real-analytic modular forms. We study the properties of our real-analytic objects in detail and give explicit examples to a fixed order in the alpha ' -expansion. In particular, our solution allows for a counting of linearly independent modular graph forms at a given weight, confirming previous partial results and giving predictions for higher, hitherto unexplored weights. It also sheds new light on the topic of uniform transcendentality of the alpha ' -expansion.
17.	Gerken, Jan, 1991, et al. (författare) Towards closed strings as single-valued open strings at genus one 2022 Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8121 .- 1751-8113. ; 55:2 Tidskriftsartikel (refereegranskat)abstract We relate the low-energy expansions of world-sheet integrals in genus-one amplitudes of open- and closed-string states. The respective expansion coefficients are elliptic multiple zeta values (eMZVs) in the open-string case and non-holomorphic modular forms dubbed 'modular graph forms (MGFs)' for closed strings. By inspecting the differential equations and degeneration limits of suitable generating series of genus-one integrals, we identify formal substitution rules mapping the eMZVs of open strings to the MGFs of closed strings. Based on the properties of these rules, we refer to them as an elliptic single-valued map which generalizes the genus-zero notion of a single-valued map acting on MZVs seen in tree-level relations between the open and closed string.
18.	Gomis, Joaquim, et al. (författare) Galilean free Lie algebras 2019 Ingår i: Journal of High Energy Physics. - : Springer. - 1029-8479 .- 1126-6708. ; 2019:9 Tidskriftsartikel (refereegranskat)abstract We construct free Lie algebras which, together with the algebra of spatial rotations, form infinite-dimensional extensions of finite-dimensional Galilei Maxwell algebras appearing as global spacetime symmetries of extended non-relativistic objects and non-relativistic gravity theories. We show how various extensions of the ordinary Galilei algebra can be obtained by truncations and contractions, in some cases via an affine Kac-Moody algebra. The infinite-dimensional Lie algebras could be useful in the construction of generalized Newton-Cartan theories gravity theories and the objects that couple to them.
19.	Gomis, Joaquim, et al. (författare) Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity 2020 Ingår i: Journal of High Energy Physics. - : Springer. - 1029-8479 .- 1126-6708. ; 2020:2 Tidskriftsartikel (refereegranskat)abstract We construct finite- and infinite-dimensional non-relativistic extensions of the Newton-Hooke and Carroll (A)dS algebras using the algebra expansion method, starting from the (anti-)de Sitter relativistic algebra in D dimensions. These algebras are also shown to be embedded in different affine Kac-Moody algebras. In the three-dimensional case, we construct Chern-Simons actions invariant under these symmetries. This leads to a sequence of non-relativistic gravity theories, where the simplest examples correspond to extended Newton-Hooke and extended (post-)Newtonian gravity together with their Carrollian counterparts.
20.	Gomis, Joaquim, et al. (författare) Symmetries of M-theory and free Lie superalgebras 2019 Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :3 Tidskriftsartikel (refereegranskat)abstract We study systematically various extensions of the Poincare superalgebra. The most general structure starting from a set of spinorial supercharges Q is a free Lie superalgebra that we discuss in detail. We explain how this universal extension of the Poincare superalgebra gives rise to many other algebras as quotients, some of which have appeared previously in various places in the literature. In particular, we show how some quotients can be very neatly related to Borcherds superalgebras. The ideas put forward also offer some new angles on exotic branes and extended symmetry structures in M-theory.
21.	Gourevitch, Dmitry, et al. (författare) Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups 2022 Ingår i: Canadian Journal of Mathematics. - 1496-4279 .- 0008-414X. ; 74:1, s. 122-169 Tidskriftsartikel (refereegranskat)abstract In this paper, we analyze Fourier coefficients of automorphic forms on a finite cover G of an adelic split simply-laced group. Let ππ be a minimal or next-to-minimal automorphic representation of G. We prove that any η∈πη∈π is completely determined by its Whittaker coefficients with respect to (possibly degenerate) characters of the unipotent radical of a fixed Borel subgroup, analogously to the Piatetski-Shapiro–Shalika formula for cusp forms on GLnGLn . We also derive explicit formulas expressing the form, as well as all its maximal parabolic Fourier coefficient, in terms of these Whittaker coefficients. A consequence of our results is the nonexistence of cusp forms in the minimal and next-to-minimal automorphic spectrum. We provide detailed examples for G of type D5D5 and E8E8 with a view toward applications to scattering amplitudes in string theory.
22.	Gustafsson, Henrik, 1988, et al. (författare) Small automorphic representations and degenerate Whittaker vectors 2016 Ingår i: Journal of Number Theory. - : Elsevier BV. - 0022-314X .- 1096-1658. ; 166, s. 344-399 Tidskriftsartikel (refereegranskat)abstract We investigate Fourier coefficients of automorphic forms on split simply-laced Lie groups G. We show that for automorphic representations of small Gelfand-Kirillov dimension the Fourier coefficients are completely determined by certain degenerate Whittaker vectors on G. Although we expect our results to hold for arbitrary simply-laced groups, we give complete proofs only for G=SL(3) and G=SL(4). This is based on a method of Ginzburg that associates Fourier coefficients of automorphic forms with nilpotent orbits of G. Our results complement and extend recent results of Miller and Sahi. We also use our formalism to calculate various local (real and p-adic) spherical vectors of minimal representations of the exceptional groups E_6, E_7, E_8 using global (adelic) degenerate Whittaker vectors, correctly reproducing existing results for such spherical vectors obtained by very different methods.
23.	Kleinschmidt, Axel, et al. (författare) K(E9) from K(E10) 2007 Ingår i: Journal of High Energy Physics (JHEP). - : IOP Publishing. - 1126-6708 .- 1029-8479. ; :6 Tidskriftsartikel (refereegranskat)abstract We analyse the M-theoretic generalisation of the tangent space structure group after reduction of the D = 11 supergravity theory to two space-time dimensions in the context of hidden Kac-Moody symmetries. The action of the resulting infinite-dimensional 'R symmetry' group K(E-9) on certain unfaithful, finite-dimensional spinor representations inherited from K(E-10) is studied. We explain in detail how these representations are related to certain finite codimension ideals within K(E-9), which we exhibit explicitly, and how the known, as well as new finite-dimensional 'generalised holonomy groups' arise as quotients of K(E-9) by these ideals. In terms of the loop algebra realisations of E-9 and K(E-9) on the fields of maximal supergravity in two space-time dimensions, these quotients are shown to correspond to (generalised) evaluation maps, in agreement with previous results of [1]. The outstanding question is now whether the related unfaithful representations of K(E-10) can be understood in a similar way.
24.	Kleinschmidt, Axel, et al. (författare) Modular realizations of hyperbolic Weyl groups 2012 Ingår i: Advances in Theoretical and Mathematical Physics. - : International Press. - 1095-0761 .- 1095-0753. ; 16:1, s. 97-148 Tidskriftsartikel (refereegranskat)abstract We study the recently discovered isomorphisms between hyperbolic Weyl groups and modular groups over integer domains in normed division algebras. We show how to realize the group action via fractional linear transformations on generalized upper half-planes over the division algebras, focusing on the cases involving quaternions and octonions. For these we construct automorphic forms, whose explicit expressions depend crucially on the underlying arithmetic properties of the integer domains. Another main new result is the explicit octavian realization of W+(E-10), which contains as a special case a new realization of W+(E-8) in terms of unit octavians and their automorphism group.
25.	Kleinschmidt, Axel, et al. (författare) Oxidizing Borcherds symmetries 2013 Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :3 Tidskriftsartikel (refereegranskat)abstract The tensor hierarchy of maximal supergravity in D dimensions is known to be closely related to a Borcherds (super) algebra that is constructed from the global symmetry group E11-D. We here explain how the Borcherds algebras in different dimensions are embedded into each other and can be constructed from a unifying Borcherds algebra. The construction also has a natural physical explanation in terms of oxidation. We then go on to show that the Hodge duality that is present in the tensor hierarchy has an algebraic counterpart. For D > 8 the Borcherds algebras we find differ from the ones existing in the literature although they generate the same tensor hierarchy.
26.	Nilsson, Bengt E W, 1952, et al. (författare) Instanton Corrections to the Universal Hypermultiplet and Automorphic Forms on SU(2,1). 2010 Ingår i: Communications in Number Theory and Physics. - 1931-4531 .- 1931-4523. ; 4:1, s. 187-266 Tidskriftsartikel (refereegranskat)abstract Abstract: The hypermultiplet moduli space in Type IIA string theory compactified on a rigid Calabi-Yau threefold X , corresponding to the “universal hypermultiplet”, is described at tree-level by the symmetric space SU(2,1)/(SU(2)×U(1)). To determine the quantum corrections to this metric, we posit that a discrete subgroup of the continuous tree-level isometry group SU(2,1), namely the Picard modular group SU(2,1;Z[i]), must remain un- broken in the exact metric – including all perturbative and non-perturbative quantum cor- rections. This assumption is expected to be valid when X admits complex multiplication by Z[i]. Based on this hypothesis, we construct an SU(2,1;Z[i])-invariant, non-holomorphic Eisenstein series, and tentatively propose that this Eisenstein series provides the exact contact potential on the twistor space over the universal hypermultiplet moduli space. We analyze its non-Abelian Fourier expansion, and show that the Abelian and non-Abelian Fourier coefficients take the required form for instanton corrections due to Euclidean D2- branes wrapping special Lagrangian submanifolds, and to Euclidean NS5-branes wrapping the entire Calabi-Yau threefold, respectively. While this tentative proposal fails to repro- duce the correct one-loop correction, the consistency of the Fourier expansion with physics expectations provides strong support for the usefulness of the Picard modular group in constraining the quantum moduli space.
27.	Nilsson, Bengt E W, 1952, et al. (författare) Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons 2010 Ingår i: roceedings of 6th International Symposium on Quantum Theory and Symmetries (QTS6), Lexington, Kentucky, 20-25 Jul 2009.. Konferensbidrag (refereegranskat)abstract Abstract.Type IIA string theory compactified on a rigid Calabi-Yau threefold gives rise to a classical moduli space that carries an isometric action of U(2,1). Various quantum corrections break this continuous isometry to a discrete subgroup. Focussing on the case where the intermediate Jacobian of the Calabi-Yau admits complex multiplication by the ring of quadratic imaginary integers Od, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2,1;Od). Based on this proposal we construct an Eisenstein series invariant under this duality group and study its non-Abelian Fourier expansion. This allows the prediction of non-perturbative effects, notably the contribution of D2- and NS5-brane instantons. The present work extends our previous analysis in 0909.4299 which was restricted to the special case of the Gaussian integers O1 = Z[i].
28.	Persson, Daniel, 1978, et al. (författare) Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4 2009 Ingår i: Journal of High Energy Physics. - : Springer Science and Business Media LLC. - 1029-8479 .- 1126-6708. Tidskriftsartikel (refereegranskat)abstract We study the symmetries of pure N=2 supergravity in D=4. As is known, this theory reduced on one Killing vector is characterised by a non-linearly realised symmetry SU(2,1) which is a non-split real form of SL(3,C). We consider the BPS brane solutions of the theory preserving half of the supersymmetry and the action of SU(2,1) on them. Furthermore we provide evidence that the theory exhibits an underlying algebraic structure described by the Lorentzian Kac-Moody group SU(2,1)^{+++}. This evidence arises both from the correspondence between the bosonic space-time fields of N=2 supergravity in D=4 and a one-parameter sigma-model based on the hyperbolic group SU(2,1)^{++}, as well as from the fact that the structure of BPS brane solutions is neatly encoded in SU(2,1)^{+++}. As a nice by-product of our analysis, we obtain a regular embedding of the Kac-Moody algebra su(2,1)^{+++} in e_{11} based on brane physics.
29.	Persson, Daniel, 1978, et al. (författare) Instanton Corrections to the Universal Hypermultiplet and Automorphic Forms on SU(2,1) 2009 Ingår i: Preprint: arXiv:0909.4299 [hep-th]. ; , s. 55 pages- Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract The hypermultiplet moduli space in Type IIA string theory compactified on a rigid Calabi-Yau threefold X, corresponding to the "universal hypermultiplet", is described at tree-level by the symmetric space SU(2,1)/(SU(2) x U(1)). To determine the quantum corrections to this metric, we posit that a discrete subgroup of the continuous tree-level isometry group SU(2,1), namely the Picard modular group SU(2,1;Z[i]), must remain unbroken in the exact metric -- including all perturbative and non perturbative quantum corrections. This assumption is expected to be valid when X admits complex multiplication by Z[i]. Based on this hypothesis, we construct an SU(2,1;Z[i])-invariant, non-holomorphic Eisenstein series, and tentatively propose that this Eisenstein series provides the exact contact potential on the twistor space over the universal hypermultiplet moduli space. We analyze its non-Abelian Fourier expansion, and show that the Abelian and non-Abelian Fourier coefficients take the required form for instanton corrections due to Euclidean D2-branes wrapping special Lagrangian submanifolds, and to Euclidean NS5-branes wrapping the entire Calabi-Yau threefold, respectively. While this tentative proposal fails to reproduce the correct one-loop correction, the consistency of the Fourier expansion with physics expectations provides strong support for the utility of the Picard modular group in constraining the quantum moduli space.
30.	Persson, Daniel, 1978, et al. (författare) Massive Type IIA Supergravity and E10 2009 Ingår i: Fortschritte der Physik. - : Wiley. - 0015-8208 .- 1521-3978. ; 57:5-7, s. 580-586 Tidskriftsartikel (refereegranskat)abstract In this talk we investigate the symmetry under E10 of Romans' massive type IIA supergravity. We show that the dynamics of a spinning particle in a non-linear sigma model on the coset space E10/K(E10) reproduces the bosonic and fermionic dynamics of massive IIA supergravity, in the standard truncation. In particular, we identify Romans' mass with a generator of E10 that is beyond the realm of the generators of E10 considered in the eleven-dimensional analysis, but using the same, underformed sigma model. As a consequence, this work provides a dynamical unification of the massless and massive versions of type IIA supergravity inside E10.
31.	Persson, Daniel, 1978, et al. (författare) On the E10/Massive Type IIA Supergravity Correspondence 2009 Ingår i: Physical Review D - Particles, Fields, Gravitation and Cosmology. - 2470-0010 .- 2470-0029. ; 79:4, s. 045088- Tidskriftsartikel (refereegranskat)abstract In this paper we investigate in detail the correspondence between E10 and Romans' massive deformation of type IIA supergravity. We analyse the dynamics of a non-linear sigma model for a spinning particle on the coset space E10/K(E10) and show that it reproduces the dynamics of the bosonic as well as the fermionic sector of the massive IIA theory, within the standard truncation. The mass deformation parameter corresponds to a generator of E10 outside the realm of the generators entering the usual D=11 analysis, and is naturally included without any deformation of the coset model for E10/K(E10). Our analysis thus provides a dynamical unification of the massless and massive versions of type IIA supergravity inside E10. We discuss a number of additional and general features of relevance in the analysis of any deformed supergravity in the correspondence to Kac-Moody algebras, including recently studied deformations where the trombone symmetry is gauged.

Skapa referenser, mejla, bekava och länka

Länka till träfflistan

Träfflista för sökning "WFRF:(Kleinschmidt Axel) "

Avgränsa träffmängd

År