Thermodynamic Geometry of Yang–Mills Vacua

Abstract

We study vacuum fluctuation properties of an ensemble of S U ( N ) gauge theory configurations, in the limit of many colors, viz. N c → ∞ , and explore the statistical nature of the topological susceptibility by analyzing its critical behavior at a non-zero-vacuum parameter θ and temperature T. We find that the system undergoes a vacuum phase transition at the chiral symmetry restoration temperature as well as at an absolute value of θ . On the other hand, the long-range correlation length solely depends on θ for the theories with critical exponent e = 2 or T = T d + 1 , where T d is the decoherence temperature. Furthermore, it is worth noticing that the unit-critical exponent vacuum configuration corresponds to a non-interacting statistical basis pertaining to a constant mass of η ′ .

Keywords

• thermodynamic geometry
• fluctuation theory
• phase transitions
• topological susceptibility
• QCD
• large N gauge theory