Chiral symmetry breaking with no bilinear condensate revisited

While chiral symmetry breaking in the QCD vacuum is attributed to nonzero chiral condensate, an alternative symmetry breaking pattern with no chiral condensate is also possible, as pointed out by Stern. This hypothetical phase was excluded in QCD at zero density long time ago, but nothing forbids it at finite baryon density. In this work, we study the $\theta$ dependence of this unorthodox phase on the basis of chiral perturbation theory. Physical observables such as energy density, topological susceptibility, non-local chiral order parameter and meson masses are computed analytically in the epsilon-regime. At nonzero $\theta$ we find an exotic phase that breaks vectorial flavor symmetries in a way analogous to the Aoki phase in lattice QCD.Comment: 27 pages, 8 figures. v2: minor revisions, published versio

Chiral dynamics in a magnetic field from the functional renormalization group

We investigate the quark-meson model in a magnetic field using the exact functional renormalization group equation beyond the local-potential approximation. Our truncation of the effective action involves anisotropic wave function renormalization for mesons, which allows us to investigate how the magnetic field distorts the propagation of neutral mesons. Solving the flow equation numerically, we find that the transverse velocity of mesons decreases with the magnetic field at all temperatures, which is most prominent at zero temperature. The meson screening masses and the pion decay constants are also computed. The constituent quark mass is found to increase with magnetic field at all temperatures, resulting in the crossover temperature that increases monotonically with the magnetic field. This tendency is consistent with most model calculations but not with the lattice simulation performed at the physical point. Our work suggests that the strong anisotropy of meson propagation may not be the fundamental origin of the inverse magnetic catalysis.Comment: 37 pages, 10 figures. v2: References added, the version published in JHE

Structure of Lefschetz thimbles in simple fermionic systems

The Picard-Lefschetz theory offers a promising tool to solve the sign problem in QCD and other field theories with complex path-integral weight. In this paper the Lefschetz-thimble approach is examined in simple fermionic models which share some features with QCD. In zero-dimensional versions of the Gross-Neveu model and the Nambu-Jona-Lasinio model, we study the structure of Lefschetz thimbles and its variation across the chiral phase transition. We map out a phase diagram in the complex four-fermion coupling plane using a thimble decomposition of the path integral, and demonstrate an interesting link between anti-Stokes lines and Lee-Yang zeros. In the case of nonzero mass, it is shown that the approach to the chiral limit is singular because of intricate cancellation between competing thimbles, which implies the necessity to sum up multiple thimbles related by symmetry. We also consider a Chern-Simons theory with fermions in $0+1$-dimension and show how Lefschetz thimbles solve the complex phase problem caused by a topological term. These prototypical examples would aid future application of this framework to bona fide QCD.Comment: 37 pages, 17 figures. v2: minor changes, the version to appear in JHE

U(1) axial symmetry and Dirac spectra in QCD at high temperature

We derive some exact results concerning the anomalous U(1)$_A$ symmetry in the chirally symmetric phase of QCD at high temperature. We discuss the importance of topology and finite-volume effects on the U(1)$_A$ symmetry violation characterized by the difference of chiral susceptibilities. In particular, we present a reliable method to measure the anomaly strength in lattice simulations with fixed topology. We also derive new spectral sum rules and a novel Banks-Casher-type relation. Through our spectral analysis we arrive at a simple alternative proof of the Aoki-Fukaya-Taniguchi "theorem" on the effective restoration of the U(1)$_A$ symmetry at high temperature.Comment: 28 pages, 2 figures; v2: Section 2 was substantially rewritten and Section 4 was omitted. published versio