Vacuum energy and $\theta$--vacuum

TL;DR

This paper investigates the vacuum energy dependence on the theta parameter in gauge theories, clarifying the presence or absence of singularities at specific values, with implications for cosmology.

Contribution

It provides a continuum non-perturbative analysis showing smooth vacuum energy dependence on theta at critical points, resolving longstanding debates.

Findings

No first order cusp singularities at θ=0 and θ=π in some gauge theories

Smooth vacuum energy dependence may influence cosmological issues

Clarifies the role of CP symmetry breaking in gauge theory vacua

Abstract

The highly non-trivial structure of the $\theta$--vacuum encodes many of the fundamental properties of gauge theories. In particular, the response of the vacuum to the $\theta$--term perturbation is sensitive to the existence of confinement, chiral symmetry breaking, etc. We analyze the dependence of the vacuum energy density on theta around two special values, $\theta=0$ and $\theta=\pi$. The existence or not of singular behaviors associated to spontaneous breaking of CP symmetry in these vacua has been a controversial matter for years. We clarify this important problem by means of continuum non-perturbative techniques. The results show the absence of first order cusp singularities on the vacuum energy density at $\theta=0$ and $\theta=\pi$ for some gauge theories. This smooth dependence of the energy on $\theta$ might have implications for long standing cosmological problems like the baryonic asymmetry and the cosmological constant problem.