AGT/Z$_2$
Abstract
We relate Liouville/Toda CFT correlators on Riemann surfaces with boundaries and cross-cap states to supersymmetric observables in four-dimensional N=2 gauge theories. Our construction naturally involves four-dimensional theories with fields defined on different Z quotients of the sphere (hemisphere and projective space) but nevertheless interacting with each other. The six-dimensional origin is a Z quotient of the setup giving rise to the usual AGT correspondence. To test the correspondence, we work out the RP partition function of four-dimensional N=2 theories by combining a 3d lens space and a 4d hemisphere partition functions. The same technique reproduces known RP partition functions in a form that lets us easily check two-dimensional Seiberg-like dualities on this nonorientable space. As a bonus we work out boundary and cross-cap wavefunctions in Toda CFT.
Cite
@article{arxiv.1708.04631,
title = {AGT/Z$_2$},
author = {Bruno Le Floch and Gustavo J. Turiaci},
journal= {arXiv preprint arXiv:1708.04631},
year = {2018}
}
Comments
56 pages. v2: Clarify discrete theta angle. v3: Published in JHEP; extra references. v4: Minor sign fix; extra references