Bosonic Partition Functions

TL;DR

This paper explores how bosonic partition functions in lattice QCD can exhibit spontaneous chiral symmetry breaking in two dimensions, challenging the Coleman-Mermin-Wagner theorem due to noncompact symmetry groups.

Contribution

It demonstrates that bosonic determinants in partition functions allow for symmetry breaking in low dimensions, supported by comparisons between bosonic and fermionic models at nonzero chemical potential.

Findings

Bosonic partition functions exhibit noncompact chiral symmetry groups.

Spontaneous symmetry breaking occurs in bosonic models at nonzero chemical potential.

Results align with theoretical predictions about nonamenable symmetries.

Abstract

The behavior of quenched Dirac spectra of two-dimensional lattice QCD is consistent with spontaneous chiral symmetry breaking which is forbidden according to the Coleman-Mermin-Wagner theorem. One possible resolution of this paradox is that, because of the bosonic determinant in the partially quenched partition function, the conditions of this theorem are violated allowing for spontaneous symmetry breaking in two dimensions or less. This goes back to work by Niedermaier and Seiler on nonamenable symmetries of the hyperbolic spin chain and earlier work by two of the auhtors on bosonic partition functions at nonzero chemical potential. In this talk we discuss chiral symmetry breaking for the bosonic partition function of QCD at nonzero isospin chemical potential and a bosonic random matrix theory at imaginary chemical potential and compare the results with the fermionic counterpart. In both cases the chiral symmetry group of the bosonic partition function is noncompact.