IAS Physics Group Meeting
Massive Deformations of SCFTs from Quantum Groups
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Abstract: A large family of four dimensional N=2 superconformal field theories (SCFTs) known as class S was constructed by Gaiotto as a (twisted) compactification of the six-dimensional N=(2,0) SCFTs labeled by an ADE Lie algebra, together with a collection of codimension-two defects on a punctured Riemann surface. Meanwhile, the Alday-Gaiotto-Tachikawa correspondence suggests the existence of a dictionary between massive deformations of these class S theories and certain (possibly degenerate) primaries of 2d Toda CFTs on the Riemann surface. To this day, determining the dictionary has remained an open problem, but we will explain that it can be elegantly derived from the representation theory of quantum affine algebras. In this pedagogical presentation, no previous knowledge of quantum groups or W-algebras (the symmetry algebra of Toda) will be assumed. The talk will serve as a pedagogical review of all the ingredients mentioned in this abstract.