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

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-$S^4$. By specializing to $SU(2)$ superconformal quivers, we show that these, together with hemi-$S^4$ 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.

Cited by in corpus (2)

• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills