Domain Walls and Decay Rate of the Excited Vacua in the Large N Yang-Mills Theory

TL;DR

This paper investigates the decay rates of excited vacua in large N Yang-Mills theory, revealing a decay rate exponentially suppressed by N to the fourth power, linked to domain wall tensions.

Contribution

It provides a field-theoretic estimate of vacuum decay rates in large N Yang-Mills theory, connecting domain wall tension to decay suppression.

Findings

Decay rate scales as exp(-const × N^4)

Domain wall tension is proportional to N

Decay suppression increases rapidly with N

Abstract

In the (non-supersymmetric) Yang-Mills theory in the large N limit there exists an infinite set of non-degenerate vacua. The distinct vacua are separated by domain walls whose tension determines the decay rate of the false vacua. I discuss the phenomenon from a field-theoretic point of view, starting from supersymmetric gluodynamics and then breaking supersymmetry, by introducing a gluino mass. By combining previously known results, the decay rate of the excited vacua is estimated, \Gamma \sim \exp (-const \times N^4). The fourth power of N in the exponent is a consequence of the fact that the wall tension is proportional to N.