The phase diagram of confining holographic theories on constant curvature manifolds in the presence of a $\theta$-angle

TL;DR

This paper explores the phase structure of confining holographic QFTs with a $ heta$-angle on constant curvature manifolds, revealing diverse phase behaviors and a Vafa-Witten-like theorem at $ heta=0$.

Contribution

It provides a comprehensive analysis of the phase diagram for confining holographic theories with a $ heta$-angle on various curvature manifolds, including new phase transition insights.

Findings

Single QFT solutions dominate the path integral with no phase transitions on negatively curved manifolds.

Positive curvature manifolds exhibit both first and second order phase transitions depending on parameters.

A holographic Vafa-Witten-like theorem is proven at $ heta=0$.

Abstract

Large families of confining holographic QFTs, described by Einstein-Dilaton gravity, are considered on constant-curvature manifolds in the presence of a $\theta$-angle. The space of ground states of such theories is explored as a function of the UV parameters, namely the dimensionless curvature and the $\theta$ angle. The free energy is computed, and the phase structure is determined. For constant negative curvature manifolds, we find solutions dual to single QFTs as well as solutions describing interfaces. The single QFTs exhibit an infinite family of saddle points, with the leading one dominating the gravitational path integral and no phase transitions present. For constant positive curvature manifolds, like de Sitter, the ($\theta$-angle, curvature) phase diagram exhibits both first and second order phase transitions, as a function of the class of theories considered. We also show that when $\theta=0$, a holographic Vafa-Witten-like theorem can be proven.