Generalized Toda Theory from Six Dimensions and the Conifold

Abstract

Recently, a physical derivation of the Alday-Gaiotto-Tachikawa correspondence has been put forward. A crucial role is played by the complex Chern-Simons theory arising in the 3d-3d correspondence, whose boundary modes lead to Toda theory on a Riemann surface. We explore several features of this derivation and subsequently argue that it can be extended to a generalization of the AGT correspondence. The latter involves codimension two defects in six dimensions that wrap the Riemann surface. We use a purely geometrical description of these defects and find that the generalized AGT setup can be modeled in a pole region using generalized conifolds. Furthermore, we argue that the ordinary conifold clarifies several features of the derivation of the original AGT correspondence.

27+2 pages, 3 figures

References in corpus (10)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• On D=5 super Yang-Mills theory and (2,0) theory
• Instanton counting with a surface operator and the chain-saw quiver
• A direct proof of AGT conjecture at beta = 1
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
• On W-algebras and the symmetries of defects of 6d N=(2,0) theory
• Relating Conifold Geometries to NS5-branes