The QCD sign problem as a total derivative

TL;DR

This paper investigates the distribution of the fermion determinant's phase in QCD at finite chemical potential, revealing that exponential cancellations due to the sign problem are total derivatives and that the baryon number measurement is orthogonal to this noise, informing lattice simulation methods.

Contribution

It demonstrates that the sign problem's exponential cancellations are total derivatives and establishes a self-consistency criterion for baryon number measurements in lattice QCD.

Findings

Exponential cancellations are total derivatives.

Baryon number is orthogonal to the sign problem noise.

Provides a criterion for lattice simulation accuracy.

Abstract

We consider the distribution of the complex phase of the fermion determinant in QCD at nonzero chemical potential and examine the physical conditions under which the distribution takes a Gaussian form. We then calculate the baryon number as a function of the complex phase of the fermion determinant and show 1) that the exponential cancellations produced by the sign problem take the form of total derivatives 2) that the full baryon number is orthogonal to this noise. These insights allow us to define a self-consistency requirement for measurements of the baryon number in lattice simulations.