Confinement in Holographic Theories at Finite Theta

TL;DR

This paper models the effects of a non-zero vacuum angle on a confining gauge theory's phase transition using holography, revealing how the vacuum angle influences critical temperature, transition dynamics, and gravitational wave signals.

Contribution

It introduces a simplified holographic model incorporating vacuum angle effects, demonstrating quadratic reduction of critical temperature and impact on transition rates and gravitational wave phenomenology.

Findings

Critical temperature decreases quadratically with vacuum angle.

Topological susceptibility sharply drops across the phase transition.

Vacuum angle variations can induce supercooling and alter gravitational wave signals.

Abstract

A strongly coupled confining gauge theory with a non-zero vacuum angle undergoing a deconfinement to confinement phase transition is studied in the holographic gravitational description. A simplified five-dimensional setup is constructed where a bulk scalar models the effect of the vacuum angle, and the suitable boundary conditions on the ultra-violet (UV) and the infra-red (IR) boundaries are identified. The IR boundary condition is motivated by higher dimensional examples where the bulk scalar comes from a Wilson loop on a shrinking cycle. In this five-dimensional dual geometry, and in the limit of small backreaction in the infra-red, the critical temperature for the phase transition is shown to reduce quadratically with the vacuum angle, matching lattice results. The topological susceptibility has a sharp reduction across the critical temperature, also matching lattice results. The rate for the phase transition is estimated as a function of the vacuum angle, and is seen to be enhanced (reduced) when the field theory has a relevant (irrelevant) deformation at high energies. Crucially, for the irrelevant case, the confined phase can get destabilized for a range of parameters. In the context of early universe dynamics, if the vacuum angle is time-dependent, the transition history changes strongly: the deconfined phase can last till much lower temperatures than naively expected, and one can trigger a transition to the confined phase by a change in the vacuum angle, thus providing a controlled way to generate supercooling. As a phenomenological application, the peak frequency and the power of resulting gravitational wave signal from bubble collisions change, affecting their visibility in detectors. Possible generalizations of the scenario are discussed.