QCD With A Chemical Potential, Topology, And The 't Hooft 1/N Expansion

TL;DR

This paper explores how observables in large-N QCD depend on chemical potential using the worldline formalism, analyzing phases, the sign problem, and planar equivalence between different chemical potentials.

Contribution

It introduces a 1/N expansion approach to study chemical potential effects in large-N QCD and clarifies the origin of the sign problem in this context.

Findings

Sign problem occurs at subleading order for C-even observables.

Planar equivalence relates QCD with baryon and isospin chemical potentials.

Analysis covers both hadronic and deconfining phases.

Abstract

We discuss the dependence of observables on the chemical potential in 't Hooft's large-N QCD. To this end we use the worldline formalism to expand the fermionic determinant in powers of 1/N. We consider the hadronic as well as the deconfining phase of the theory. We discuss the origin of the sign problem in the worldline approach and elaborate on the planar equivalence between QCD with a baryon chemical potential and QCD with an isospin chemical potential. We show that for C-even observables the sign problem occurs at a subleading order in the 1/N expansion of the fermionic determinant. Finally, we comment on the finite N theory.