2013/09/06 by Mina Aganagic, Aganagic, Mina, Nathan Haouzi +5 · 1 citation
Physics and Astronomy · #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Chromodynamics and Particle Interactions #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1309.1687
openalex publication_date 2013/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Conformal blocks of Liouville theory have a Coulomb-gas representation as Dotsenko-Fateev (DF) integrals over the positions of screening charges. For q-deformed Liouville, the conformal blocks on a sphere with an arbitrary number of punctures are manifestly the same, when written in DF representation, as the partition functions of a class of 3d U(N) gauge theories with N=2 supersymmetry, in the Omega-background. Coupling the 3d gauge theory to a flavor in fundamental representation corresponds to inserting a Liouville vertex operator; the two real mass parameters determine the momentum and position of the puncture. The DF integrals can be computed by residues. The result is the instanton sum of a five dimensional N=1 gauge theory. The positions of the poles are labeled by tuples of partitions, the residues of the integrand are the Nekrasov summands.