19,497 research outputs found
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 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 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
Partial regularity for parabolic systems with VMO-coefficients
We establish partial regularity for vector-valued solutions to parabolic
systems where the coefficients are possibly discontinuous with respect to
(x,t). More precisely, we assume a VMO-condition with respect to the (x,t) and
continuity with respect to u and prove H\"older continuity of the solutions
outside of singular sets.Comment: 16pages. arXiv admin note: text overlap with arXiv:1302.414
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 -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) 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) 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) symmetry at high temperature.Comment: 28 pages, 2 figures; v2: Section 2 was substantially rewritten and
Section 4 was omitted. published versio
- …