Agt/ℤ 2
Bruno Floch (0000 0001 2097 5006, Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, 08544, U.S.A.)
; Gustavo Turiaci (0000 0001 2097 5006, Physics Department, Princeton University, Princeton, NJ, 08544, U.S.A.)
We relate Liouville/Toda CFT correlators on Riemann surfaces with boundaries and cross-cap states to supersymmetric observables in four-dimensional N = 2 $$ \mathcal{N}=2 $$ 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 $$ \mathcal{N}=2 $$ theories by combining a 3d lens space and a 4d hemisphere partition functions. The same technique reproduces known ℝℙ 2 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.
