QCD at a Finite Density of Static Quarks

TL;DR

This paper explores cluster methods and partial re-summation techniques to address sign problems in quantum chromodynamics (QCD) at finite density, demonstrating solutions in static quark limits and suggesting future directions for more complex cases.

Contribution

It introduces a new approach using cluster methods and partial re-summation to tackle sign problems in QCD, especially at finite density with static quarks.

Findings

Sign problem simplifies with static quarks due to decoupling.

Complete solution possible when gauge dynamics is replaced by a Potts model.

New approach indicates potential for solving more complex sign problems in QCD.

Abstract

Recently, cluster methods have been used to solve a variety of sign problems including those that arise in the presence of fermions. In all cases an analytic partial re-summation over a class of configurations in the path integral was necessary. Here the new ideas are illustrated using the example of QCD at a finite density of static quarks. In this limit the sign problem simplifies since the fermionic part decouples. Furthermore, the problem can be solved completely when the gauge dynamics is replaced by a Potts model. On the other hand in QCD with light quarks the solution will require a partial re-summation over both fermionic and gauge degrees of freedom. The new approach points to unexplored directions in the search for a solution to this more challenging sign problem.