Abstract
We demonstrate the existence of an anomaly-induced inhomogeneous phase in a class of vectorlike gauge theories without the sign problem, thus disproving the long-standing conjecture that the absence of the 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 an external magnetic field. Our results provide a benchmark for future lattice studies of inhomogeneous phases in dense quark matter.
Highlights
Introduction.—Self-organization of matter into inhomogeneous patterns is ubiquitous in nature; after all, most natural materials develop crystalline order at sufficiently low temperatures
Various nonuniform phases are expected to play an important role for the thermodynamics of quark matter under extreme conditions [1]
Predictions of such phases for the phase diagram of quantum chromodynamics (QCD) are, mostly based on model calculations neglecting order parameter fluctuations, which may be crucial for thestability of the phase [2]
Summary
The matrix P can be assumed unitary and symmetric for real quarks, and unitary and antisymmetric for pseudoreal quarks [14]. For a theory with the SU(2) gauge group and fundamental quarks (“two-color QCD”), P is given by a Pauli matrix in the color space, P 1⁄4 σ2. Provided the electric charges of the u and d quarks satisfy qu 1⁄4 −qd, their respective Dirac operators are related by ðKCγ5PÞDu 1⁄4 DdðKCγ5PÞ; ð1Þ
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