1. 
 Bao, Ling, 1980, et al.
(författare)

A note on topological M5branes and stringfivebrane duality
 2008

Ingår i: Journal of High Energy Physics.  10298479 . 11266708. ; :6, s. 11

Tidskriftsartikel (refereegranskat)abstract
 We derive the stability conditions for the M5brane in topological Mtheory using ksymmetry. The nonlinearly selfdual 3form on the worldvolume is necessarily nonvanishing, as is the case also for the 2form field strengths on coisotropic branes in topological string theory. It is demonstrated that the selfduality is consistent with the stability conditions, which are solved locally in terms of a tensor in the representation 6 of SU(3) subset of G(2). The double dimensional reduction of the M5brane is the D4brane, and its direct reduction is an NS5brane. We show that the equation of motion for the 3form on the NS5brane wrapping a CalabiYau space is exactly the KodairaSpencer equation, providing support for a stringfivebrane duality in topological string theory.


2. 
 Bao, Ling, 1980, et al.
(författare)

A Note on Topological M5branes and StringFivebrane Duality
 2006

Tidskriftsartikel (övrigt vetenskapligt)abstract
 We derive the stability conditions for the M5brane in topological Mtheory using kappasymmetry. The nonlinearly selfdual 3form on the worldvolume is necessarily nonvanishing, as is the case also for the 2form field strengths on coisotropic branes in topological string theory. It is demonstrated that the selfduality is consistent with the stability conditions, which are solved locally in terms of a tensor in the representation 6 of SU(3) in G_2. The double dimensional reduction of the M5brane is the D4brane, and its direct reduction is an NS5brane. We show that the equation of motion for the 3form on the NS5brane wrapping a CalabiYau space is exactly the KodairaSpencer equation, providing support for a stringfivebrane duality in topological string theory.


3. 
 Bao, Ling, 1980, et al.
(författare)

Aspects of higher curvature terms and Uduality
 2007

Ingår i: Classical and Quantum Gravity.  02649381. ; 25:9

Tidskriftsartikel (refereegranskat)abstract
 We discuss various aspects of dimensional reduction of gravity with theEinsteinHilbert action supplemented by a lowest order deformation formed asthe Riemann tensor raised to powers two, three or four. In the case of R^2 wegive an explicit expression, and discuss the possibility of extended cosetsymmetries, especially SL(n+1,Z) for reduction on an ntorus to threedimensions. Then we start an investigation of the dimensional reduction of R^3and R^4 by calculating some terms relevant for the coset formulation, aiming inparticular towards E_8(8)/(Spin(16)/Z_2) in three dimensions and aninvestigation of the derivative structure. We emphasise some issues concerningthe need for the introduction of nonscalar automorphic forms in order torealise certain expected enhanced symmetries.


4. 
 Bao, Ling, 1980
(författare)

Aspects of Wrapped Branes in String and MTheory
 2009

Doktorsavhandling (övrigt vetenskapligt)abstract
 This thesis consists of an introductory text together with five appended research papers. The Ariadne's thread through the whole thesis is various effects coming from highdimensional pbranes in various subsectors of string and Mtheory.The low energy effective actions in string and Mtheory consists of a classical supergravity together with quantum corrections. In particular the nonperturbative correction terms arise from instanton effects, which are interpreted as pbranes wrapping supersymmetric cycles. The general structure of the full effective action is the result of a complicated interplay between supersymmetry and Uduality. Requiring the action to be invariant under Uduality leads to mathematical functions called automorphic forms. Both perturbative and nonperturbative corrections seem to be captured by these functions. The Uduality groups can be found by analyzing the algebraic structures of the moduli space after toroidal compactification. Using this line of thinking, some simple examples of higher order derivative corrections in pure gravity are investigated.Compactification on manifolds with special holonomy is also discussed in this thesis, with focus on the resulting moduli spaces. Certain quantum corrections to type IIA string theory compactified on a rigid CalabiYau threefold are analyzed.Manifolds with special holonomy constitute target spaces of the topological subsectors in string and Mtheory. The low energy effective action of these theories consists of a classical contribution from a form theory of gravity, which receives quantum corrections from branes wrapping supersymmetric cycles in the target space. In particular the dynamics of the M2 and M5branes are discussed in the context of a topological version of Mtheory.


5. 
 Bao, Ling, 1980, et al.
(författare)

Kac–moody groups and automorphic forms in low dimensional supergravity theories
 2017

Ingår i: Lie Algebras, Vertex Operator Algebras, and Related Topics.  9781470426668 ; , s. 2940

Bokkapitel (övrigt vetenskapligt)abstract
 Kac–Moody groups G over ? have been conjectured to occur as symmetry groups of supergravity theories dimensionally reduced to dimensions less than 3, and their integral forms G(?) conjecturally encode quantized symmetries. In this review paper, we briefly introduce the conjectural symmetries of Kac–Moody groups in supergravity as well as the known evidence for these conjectures. We describe constructions of Kac–Moody groups over ? and ? using certain choices of fundamental modules that are considered to have physical relevance. Eisenstein series on certain finite dimensional algebraic groups are known to encode quantum corrections in the low energy limit of superstring theories. We describe briefly how the construction of Eisenstein series extends to Kac–Moody groups. The constant terms of Eisenstein series on E9, E10 and E11 are predicted to encode perturbative string theory corrections.


6. 
 Bao, Ling, 1980, et al.
(författare)

M5branes, toric diagrams and gauge theory duality
 2012

Ingår i: Journal of High Energy Physics.  10298479 . 11266708.

Tidskriftsartikel (refereegranskat)abstract
 In this article we explore the duality between the low energy effective theory of fivedimensional N = 1 SU(N)(M1) and SU(M)(N1) linear quiver gauge theories compactified on S1. The theories we study are the fivedimensional uplifts of fourdimensional superconformal linear quivers. We study this duality by comparing the SeibergWitten curves and the Nekrasov partition functions of the two dual theories. The SeibergWitten curves are obtained by minimizing the worldvolume of an M5brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these fivedimentional gauge theories are related to qdeformed Liouville and Toda SCFTs in twodimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.


7. 
 Bao, Ling, 1980, et al.
(författare)

Membranes for Topological MTheory
 2005

Ingår i: Journal of High Energy Physics.

Tidskriftsartikel (refereegranskat)abstract
 We formulate a theory of topological membranes on manifolds with G_2 holonomy. The BRST charges of the theories are the superspace Killing vectors (the generators of global supersymmetry) on the background with reduced holonomy G_2. In the absence of spinning formulations of supermembranes, the starting point is an N=2 target space supersymmetric membrane in seven euclidean dimensions. The reduction of the holonomy group implies a twisting of the rotations in the tangent bundle of the branes with ``Rsymmetry'' rotations in the normal bundle, in contrast to the ordinary spinning formulation of topological strings, where twisting is performed with internal U(1) currents of the N=(2,2) superconformal algebra. The double dimensional reduction on a circle of the topological membrane gives the strings of the topological Amodel (a byproduct of this reduction is a GreenSchwarz formulation of topological strings). We conclude that the action is BRSTexact modulo topological terms and fermionic equations of motion. We discuss the role of topological membranes in topological Mtheory and the relation of our work to recent work by Hitchin and by Dijkgraaf et al.


8. 
 Bao, Ling, 1980, et al.
(författare)

NonLagrangian theories from brane junctions
 2014

Ingår i: Journal of High Energy Physics.  10298479 . 11266708. ; :1, s. Art. no. 175

Tidskriftsartikel (refereegranskat)abstract
 In this article we use 5brane junctions to study the 5D T N SCFTs corresponding to the 5D N = 1 uplift of the 4D N = 2 strongly coupled gauge theories, which are obtained by compactifying N M5 branes on a sphere with three full punctures. Even though these theories have no Lagrangian description, by using the 5brane junctions proposed by Benini, Benvenuti and Tachikawa, we are able to derive their SeibergWitten curves and Nekrasov partition functions. We crosscheck our results with the 5D superconformal index proposed by Kim, Kim and Lee. Through the AGTW correspondence, we discuss the relations between 5D superconformal indices and n point functions of the q deformed W N Toda theories.


9. 
 Bao, Ling, 1980, et al.
(författare)

Rigid CalabiYau threefolds, Picard Eisenstein series and instantons
 2013

Ingår i: Journal of Physics: Conference Series.  17426588 . 17426596. ; 462:1

Konferensbidrag (refereegranskat)abstract
 Type IIA string theory compactified on a rigid CalabiYau 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 CalabiYau 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 nonAbelian Fourier expansion. This allows the prediction of nonperturbative effects, notably the contribution of D2 and NS5brane 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].


10. 
 Bao, Ling, 1980, et al.
(författare)

UDuality and the Compactified GaussBonnet Term
 2007

Ingår i: Journal of High Energy Physics.

Tidskriftsartikel (refereegranskat)abstract
 We present the complete toroidal compactification of the GaussBonnet Lagrangian from D dimensions to Dn dimensions. Our goal is to investigate the resulting action from the point of view of the "Uduality" symmetry SL(n+1,R) which is present in the treelevel Lagrangian when Dn=3. The analysis builds upon and extends the investigation of the paper [arXiv:0706.1183], by computing in detail the full structure of the compactified GaussBonnet term, including the contribution from the dilaton exponents. We analyze these exponents using the representation theory of the Lie algebra sl(n+1,R) and determine which representation is the relevant one for quadratic curvature corrections. By interpreting the result of the compactification as a leading term in a large volume expansion of an SL(n+1,Z)invariant action, we conclude that the overall exponential dilaton factor should not be included in the representation structure. As a consequence, all dilaton exponents correspond to weights of sl(n+1,R), which, nevertheless, remain on the positive side of the root lattice.

