Vacuum energy and θ-vacuum

Abstract

The highly non-trivial structure of the θ-vacuum encodes many of the fundamental properties of gauge theories. In particular, the response of the vacuum to the θ-term perturbation is sensitive to the existence of confinement, chiral symmetry breaking, etc. We analyze the dependence of the vacuum energy density on θ around two special values, θ = 0 and θ = π. 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 θ = 0 and θ = π for some gauge theories. This smooth dependence of the energy on θ might have implications for long standing cosmological problems like the baryonic asymmetry and the cosmological constant problem.

CP Symmetry, Lee-Yang zeros and Phase Transitions

“…In this paper we analyze the analytic structure of the QCD partition function in the complex e plane [4,5] and clarify why there is no first order phase transition at e = 0 and CP symmetry is preserved in QCD. The basic argument is that the Vafa-Witten inequality [6] is not compatible with the existence of a first order singularity in the vacuum energy density at e = 0.…”

An upper limit to the electric dipole moment of the neutron from lattice QCD

“…This hypothesis has been debated in the literature [8,9,10] and it is in fact the one which we have tried to test on the lattice for the topological charge operator.…”

Analyticity in θ and infinite volume limit of the topological susceptibility in SU(3) gauge theory

“…Recently Aguado and Asorey [5,6] have proved that parity cannot be broken by the topological charge operator Q. The vacuum energy density E(θ) is a well defined smooth function for any value of θ.…”