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ADE little string theory on a Riemann surface and conformal blocks of q-deformed W-algebras

Mathematical Physics & Probability

Speaker: Nathan Haouzi, Berkeley
Location: 2112 MSB
Start time: Wed, May 11 2016, 3:10PM

Let g be a simply-laced Lie algebra. The AGT correspondence, named after Alday, Gaiotto, and Tachikawa, relates two kinds of objects. On one hand, one studies conformal blocks of a vertex operator algebra, called W(g)-algebra, on a Riemann surface C. On the other hand, there is a six-dimensional conformal field theory, called "g-type (2,0) theory", defined on C x R^4. The AGT correspondence associates defects of this six-dimensional theory to vertex operators of the W(g)-algebra, inserted at point on C. It turns out that there is an embedding of both sides of the AGT correspondence into bigger theories, which can be seen as "mass deformations" of the original theories: the six-dimensional theory becomes the so-called six-dimensional little string, while on the W(g)-algebra side, we end up with a "q-deformed" W(g)-algebra. After these deformations, we are able to make the correspondence precise and prove it, for any g simply-laced.