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$\mathcal{N}=2$ gauge theories on unoriented/open four-manifolds and their AGT counterparts (1710.06283v1)

Published 17 Oct 2017 in hep-th, math-ph, and math.MP

Abstract: We compute the exact path integral of $\mathcal{N}=2$ supersymmetric gauge theories with general gauge group on $\mathbb{RP}4$ and a $\mathbb{Z}_2$-quotient of the hemi-$S4$. By specializing to $SU(2)$ superconformal quivers, we show that these, together with hemi-$S4$ partition functions, compute Liouville correlators on unoriented/open Riemann surfaces. We perform explicit checks for Riemann surfaces obtained as $\mathbb{Z}_2$ quotients of the sphere and the torus. We also discuss the coupled $3d!-!4d$ systems associated to Liouville amplitudes with boundary punctures.

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