AGT/Z$_2$

Understand

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$_2$ quotients of the sphere (hemisphere and projective space) but nevertheless interacting with each other.
• The six-dimensional origin is a Z$_2$ quotient of the setup giving rise to the usual AGT correspondence.
• To test the correspondence, we work out the RP$^4$ partition function of four-dimensional N=2 theories by combining a 3d lens space and a 4d hemisphere partition functions.