Vacuum energy as a c-function for theories with dynamically generated masses

TL;DR

This paper proposes that in certain gauge theories with dynamical mass generation, the vacuum energy acts as a c-function, with the beta function behavior indicating a non-trivial fixed point at the minimum of vacuum energy.

Contribution

It demonstrates that the vacuum energy serves as a c-function in theories with dynamical mass generation, linking the fixed point to the minimum of vacuum energy.

Findings

Beta function is negative up to a fixed point.

Vacuum energy has properties of a c-function.

Fixed point corresponds to the minimum of vacuum energy.

Abstract

We argue that in asymptotically free non-Abelian gauge theories possessing the phenomenon of dynamical mass generation the $\beta$ function is negative up to a value of the coupling constant that corresponds to a non-trivial fixed point, in agreement with recent AdS/QCD analysis. This fixed point happens at the minimum of the vacuum energy ($\Omega$), which, as a characteristic of theories with dynamical mass generation, has the properties of a c-function.