Bosonic Partition Functions at Nonzero (Imaginary) Chemical Potential

TL;DR

This paper investigates bosonic partition functions at nonzero imaginary chemical potential, comparing their phase transition behavior and regularization effects to fermionic counterparts, revealing conditions under which phase transitions persist or are suppressed.

Contribution

It introduces an analysis of bosonic partition functions at nonzero chemical potential and compares their phase transition properties to fermionic theories, highlighting the impact of divergence and regularization.

Findings

Fermionic phase transition persists in bosonic theory when partition functions are finite.

Divergent bosonic partition functions, after regularization, do not exhibit fermionic phase transitions.

Bosonic theories are always in the broken phase if their partition functions diverge and are regularized.

Abstract

We consider bosonic random matrix partition functions at nonzero chemical potential and compare the chiral condensate, the baryon number density and the baryon number susceptibility to the result of the corresponding fermionic partition function. We find that as long as results are finite, the phase transition of the fermionic theory persists in the bosonic theory. However, in case that bosonic partition function diverges and has to be regularized, the phase transition of the fermionic theory does not occur in the bosonic theory, and the bosonic theory is always in the broken phase.