| 1. |
- Alexandrov, Sergei, et al.
(författare)
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Wall-crossing, Rogers dilogarithm and the QK/HK correspondence
- 2011
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Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 2011:12, s. 027-
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Tidskriftsartikel (refereegranskat)abstract
- When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N=2 string vacua and the Coulomb branch of rigid N=2 gauge theories on R^3 x S^1 are strikingly similar and, to a large extent, dictated by consistency with wall-crossing. We elucidate this similarity by showing that these two spaces are related under a general duality between, on one hand, quaternion-Kahler manifolds with a quaternionic isometry and, on the other hand, hyperkahler manifolds with a rotational isometry, further equipped with a hyperholomorphic circle bundle with a connection. We show that the transition functions of the hyperholomorphic circle bundle relevant for the hypermultiplet moduli space are given by the Rogers dilogarithm function, and that consistency across walls of marginal stability is ensured by the motivic wall-crossing formula of Kontsevich and Soibelman. We illustrate the construction on some simple examples of wall-crossing related to cluster algebras for rank 2 Dynkin quivers. In an appendix we also provide a detailed discussion on the general relation between wall-crossing and the theory of cluster algebras.
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| 2. |
- Nilsson, Bengt E W, 1952, et al.
(författare)
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Instanton Corrections to the Universal Hypermultiplet and Automorphic Forms on SU(2,1).
- 2010
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Ingår i: Communications in Number Theory and Physics. - 1931-4531 .- 1931-4523. ; 4:1, s. 187-266
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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.
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| 3. |
- Nilsson, Bengt E W, 1952, et al.
(författare)
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Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons
- 2010
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Ingår i: roceedings of 6th International Symposium on Quantum Theory and Symmetries (QTS6), Lexington, Kentucky, 20-25 Jul 2009..
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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].
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| 4. |
- Persson, Daniel, 1978, et al.
(författare)
-
Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces
- 2011
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Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 1103, s. 111-
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Tidskriftsartikel (refereegranskat)abstract
- We investigate quantum corrections to the hypermultiplet moduli space M in Calabi-Yau compactifications of type II string theories, with particular emphasis on instanton effects from Euclidean NS5-branes. Based on the consistency of D- and NS5-instanton corrections, we determine the topology of the hypermultiplet moduli space at fixed string coupling, as previewed in arXiv:1009.3026. On the type IIB side, we compute corrections from (p,k)-fivebrane instantons to the metric on M (specifically, the correction to the complex contact structure on its twistor space Z) by applying S-duality to the D-instanton sum. For fixed fivebrane charge k, the corrections can be written as a non-Gaussian theta series, whose summand for k=1 reduces to the topological A-model amplitude. By mirror symmetry, instanton corrections induced from the chiral type IIA NS5-brane are similarly governed by the wave function of the topological B-model. In the course of this investigation we clarify charge quantization for coherent sheaves and find hitherto unnoticed corrections to the Heisenberg, monodromy and S-duality actions on M, as well as to the mirror map for Ramond-Ramond fields and D-brane charges.
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| 5. |
- Persson, Daniel, 1978, et al.
(författare)
-
Instanton Corrections to the Universal Hypermultiplet and Automorphic Forms on SU(2,1)
- 2009
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Ingår i: Preprint: arXiv:0909.4299 [hep-th]. ; , s. 55 pages-
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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.
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| 6. |
- Persson, Daniel, 1978, et al.
(författare)
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On the topology of the hypermultiplet moduli space in type II/CY string vacua
- 2011
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Ingår i: Physical Review D. ; 83, s. 026001-
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Tidskriftsartikel (refereegranskat)abstract
- By analyzing qualitative aspects of NS5-brane instanton corrections, we determine the topology of the hypermultiplet moduli space M_H in Calabi-Yau compactifications of type II string theories at fixed value of the dilaton and of the Calabi-Yau metric. Specifically, we show that for fivebrane instanton couplings to be well-defined, translations along the intermediate Jacobian must induce non-trivial shifts of the Neveu-Schwarz axion which had thus far been overlooked. As a result, the Neveu-Schwarz axion parametrizes the fiber of a circle bundle, isomorphic to the one in which the fivebrane partition function is valued. In the companion paper arXiv:1010.5792, we go beyond the present analysis and take steps towards a quantitative description of fivebrane instanton corrections, using a combination of mirror symmetry, S-duality, topological string theory and twistor techniques.
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| 7. |
- Persson, Daniel, 1978, et al.
(författare)
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Quantum hypermultiplet moduli spaces in N=2 string vacua: a review
- 2015
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Ingår i: Proceedings of Symposia in Pure Mathematics - Conference on String-Math 2012. - Providence, Rhode Island : American Mathematical Society. - 2324-707X. - 9780821894958 ; 90, s. 181-211
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Konferensbidrag (refereegranskat)abstract
- The hypermultiplet moduli space M_H in type II string theories compactified on a Calabi-Yau threefold X is largely constrained by supersymmetry (which demands quaternion-K\"ahlerity), S-duality (which requires an isometric action of SL(2, Z)) and regularity. Mathematically, M_H ought to encode all generalized Donaldson-Thomas invariants on X consistently with wall-crossing, modularity and homological mirror symmetry. We review recent progress towards computing the exact metric on M_H, or rather the exact complex contact structure on its twistor space.
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| 8. |
- Persson, Daniel, 1978, et al.
(författare)
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The automorphic NS5-brane
- 2009
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Ingår i: Preprint: arXiv:0902.3274 [hep-th].
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Understanding the implications of SL(2,Z) S-duality for the hypermultiplet moduli space of type II string theories has led to much progress recently in uncovering D-instanton contributions. In this work, we suggest that the extended duality group SL(3,Z), which includes both S-duality and Ehlers symmetry, may determine the contributions of D5 and NS5-branes. We support this claim by automorphizing the perturbative corrections to the "extended universal hypermultiplet", a five-dimensional universal SO(3) SL(3,R) subspace which includes the string coupling, overall volume, Ramond zero-form and six-form and NS axion. Using the non-Abelian Fourier expansion of the Eisenstein series attached to the principal series of SL(3,R), first worked out by Vinogradov and Takhtajan 30 years ago, we extract the contributions of D(-1)-D5 and NS5-brane instantons, corresponding to the Abelian and non-Abelian coefficients, respectively. In particular, the contributions of k NS5-branes can be summarized into a vector of wave functions \Psi_{k,l}, l=0... k-1, as expected on general grounds. We also point out that for more general models with a symmetric moduli space K G, the minimal theta series of G generates an infinite series of exponential corrections of the form required for "small" D(-1)-D1-D3-D5-NS5 instanton bound states. As a mathematical spin-off, we make contact with earlier results in the literature about the spherical vectors for the principal series of SL(3,R) and for minimal representations.
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