# Anomaly-Induced Inhomogeneous Phase in Quark Matter without the Sign Problem

## TL;DR

This paper shows that in certain gauge theories without sign problems, an anomaly-driven inhomogeneous phase exists, challenging previous beliefs and providing a new avenue for lattice studies of dense quark matter.

## Contribution

It demonstrates the existence of an anomaly-induced inhomogeneous phase in sign-problem-free gauge theories, countering the idea that absence of sign problem prevents spontaneous translational symmetry breaking.

## Key findings

- Inhomogeneous phase exists in sign-problem-free theories.
- The phase can be tested via neutral pion decay constant under magnetic fields.
- Provides a benchmark for lattice simulations of dense quark matter.

## Abstract

We demonstrate the existence of an anomaly-induced inhomogeneous phase in a class of vector-like gauge theories without sign problem, thus disproving the long-standing conjecture that the absence of sign problem precludes spontaneous breaking of translational invariance. The presence of the phase in the two-color modification of quantum chromodynamics can be tested by an independent nonperturbative evaluation of the neutral pion decay constant as a function of external magnetic field. Our results provide a benchmark for future lattice studies of inhomogeneous phases in dense quark matter.