Theta Dependence In The Large N Limit Of Four-Dimensional Gauge Theories

TL;DR

This paper explores how the vacuum structure of four-dimensional pure gauge theories depends on the theta parameter in the large N limit, revealing a rich landscape with spontaneous CP symmetry breaking at specific points.

Contribution

It introduces a duality-based approach to analyze theta dependence, showing the existence of infinitely many stable vacua and describing domain walls via wrapped branes.

Findings

Vacua are stable and infinitely many in the large N limit.

The true vacuum varies smoothly with theta except at pi, where it jumps.

Spontaneous CP symmetry breaking occurs at theta equals pi.

Abstract

The theta dependent of pure gauge theories in four dimensions can be studied using a duality of large N gauge theories with string theory on a certain spacetime. Via this duality, one can argue that for every theta, there are infinitely many vacua that are stable in the large N limit. The true vacuum, found by minimizing the energy in this family, is a smooth function of theta except at theta equal to pi, where it jumps. This jump is associated with spontaneous breaking of CP symmetry. Domain walls separating adjacent vacua are described in terms of wrapped sixbranes.