Please use this identifier to cite or link to this item: https://doi.org/10.1007/JHEP07(2013)171
Title: M-theoretic derivations of 4d-2d dualities: From a geometric Langlands duality for surfaces, to the AGT correspondence, to integrable systems
Authors: Tan, M.-C. 
Keywords: Conformal and W Symmetry
Differential and Algebraic Geometry
M-Theory
String Duality
Issue Date: 2013
Citation: Tan, M.-C. (2013). M-theoretic derivations of 4d-2d dualities: From a geometric Langlands duality for surfaces, to the AGT correspondence, to integrable systems. Journal of High Energy Physics 2013 (7) : -. ScholarBank@NUS Repository. https://doi.org/10.1007/JHEP07(2013)171
Abstract: In part I, we extend our analysis in [arXiv:0807.1107], and show that a mathematically conjectured geometric Langlands duality for complex surfaces in [1], and its generalizations - which relate some cohomology of the moduli space of certain ("ramified") G-instantons to the integrable representations of the Langlands dual of certain affine (sub) G-algebras, where G is any compact Lie group - can be derived, purely physically, from the principle that the spacetime BPS spectra of string-dual M-theory compactifications ought to be equivalent. In part II, to the setup in part I, we introduce Omega-deformation via fluxbranes and add half-BPS boundary defects via M9-branes, and show that the celebrated AGT correspondence in [2, 3], and its generalizations - which essentially relate, among other things, some equivariant cohomology of the moduli space of certain ("ramified") G-instantons to the integrable representations of the Langlands dual of certain affine W -algebras - can likewise be derived from the principle that the spacetime BPS spectra of string-dual M-theory compactifications ought to be equivalent. In part III, we consider various limits of our setup in part II, and connect our story to chiral fermions and integrable systems. Among other things, we derive the NekrasovOkounkov conjecture in [4] - which relates the topological string limit of the dual Nekrasov partition function for pure G to the integrable representations of the Langlands dual of an affine G-algebra - and also demonstrate that the Nekrasov-Shatashvili limit of the "fullyramified" Nekrasov instanton partition function for pure G is a simultaneous eigenfunction of the quantum Toda Hamiltonians associated with the Langlands dual of an affine G-algebra. Via the case with matter, we also make contact with Hitchin systems and the "ramified" geometric Langlands correspondence for curves. © 2013 SISSA, Trieste, Italy.
Source Title: Journal of High Energy Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/97265
ISSN: 11266708
DOI: 10.1007/JHEP07(2013)171
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