72 research outputs found
Complex path integrals and saddles in two-dimensional gauge theory
We study numerically the saddle point structure of two-dimensional (2D) lattice gauge theory, represented by the Gross-Witten-Wadia unitary matrix model. The saddle points are in general complex-valued, even though the original integration variables and action are real. We confirm the trans-series/instanton gas structure in the weak-coupling phase, and identify a new complex-saddle interpretation of non-perturbative effects in the strong-coupling phase. In both phases, eigenvalue tunneling refers to eigenvalues moving off the real interval, into the complex plane, and the weak-to-strong coupling phase transition is driven by saddle condensation
Quantum chaos, thermalization, and entanglement generation in real-time simulations of the Banks-Fischler-Shenker-Susskind matrix model
We study numerically the onset of chaos and thermalization in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model with and without fermions, considering Lyapunov exponents, entanglement generation, and quasinormal ringing. We approximate the real-time dynamics in terms of the most general Gaussian density matrices with parameters which obey self-consistent equations of motion, thus extending the applicability of real-time simulations beyond the classical limit. Initial values of these Gaussian density matrices are optimized to be as close as possible to the thermal equilibrium state of the system. Thus attempting to bridge between the low-energy regime with a calculable holographic description and the classical regime at high energies, we find that quantum corrections to classical dynamics tend to decrease the Lyapunov exponents, which is essential for consistency with the Maldacena-Shenker-Stanford bound at low temperatures. The entanglement entropy is found to exhibit an expected "scrambling" behavior-rapid initial growth followed by saturation. At least at high temperatures the entanglement saturation time appears to be governed by classical Lyapunov exponents. Decay of quasinormal modes is found to be characterized by the shortest timescale of all. We also find that while the bosonic matrix model becomes nonchaotic in the low-temperature regime, for the full BFSS model with fermions the leading Lyapunov exponent, entanglement saturation time, and decay rate of quasinormal modes all remain finite and nonzero down to the lowest temperatures
Electric conductivity in finite-density SU(2) lattice gauge theory with dynamical fermions
We study the dependence of the electric conductivity on chemical potential in
finite-density gauge theory with flavours of rooted staggered
sea quarks, in combination with Wilson-Dirac and Domain Wall valence quarks.
The pion mass is reasonably small with . We
concentrate in particular on the vicinity of the chiral crossover, where we
find the low-frequency electric conductivity to be most sensitive to small
changes in fermion density. Working in the low-density QCD-like regime with
spontaneously broken chiral symmetry, we obtain an estimate of the first
nontrivial coefficient of the expansion of conductivity in powers of ,
which has rather weak temperature dependence and takes its maximal value around the critical temperature. At larger densities and
lower temperatures, the conductivity quickly grows towards the diquark
condensation phase, and also becomes closer to the free quark result. As a
by-product of our study we confirm the conclusions of previous studies with
heavier pion that for gauge theory the ratio of crossover temperature
to pion mass at is significantly smaller than
in real QCD.Comment: 22 pages, 18 figures, RevTeX; v2: new data on larger lattices added,
results updated; published versio
Z2 electric strings and center vortices in SU(2) lattice gauge theory
We study the representations of SU(2) lattice gauge theory in terms of sums over the worldsheets of center vortices and Z2 electric strings, i.e. surfaces which open on the Wilson loop. It is shown that in contrast to center vortices the density of electric Z2 strings diverges in the continuum limit of the theory independently of the gauge fixing, however, their contribution to the Wilson loop yields physical string tension due to non-positivity of their statistical weight in the path integral, which is in turn related to the presence of Z2 topological monopoles in the theory
Quantum chaos, thermalization and entanglement generation in real-time simulations of the BFSS matrix model
We study numerically the onset of chaos and thermalization in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model with and without fermions, considering Lyapunov exponents, entanglement generation, and quasinormal ringing. We approximate the real-time dynamics in terms of the most general Gaussian density matrices with parameters which obey self-consistent equations of motion, thus extending the applicability of real-time simulations beyond the classical limit. Initial values of these Gaussian density matrices are optimized to be as close as possible to the thermal equilibrium state of the system. Thus attempting to bridge between the low-energy regime with a calculable holographic description and the classical regime at high energies, we find that quantum corrections to classical dynamics tend to decrease the Lyapunov exponents, which is essential for consistency with the Maldacena-Shenker-Stanford (MSS) bound at low temperatures. The entanglement entropy is found to exhibit an expected "scrambling" behavior - rapid initial growth followed by saturation. At least at high temperatures the entanglement saturation time appears to be governed by classical Lyapunov exponents. Decay of quasinormal modes is found to be characterized by the shortest time scale of all. We also find that while the bosonic matrix model becomes non-chaotic in the low-temperature regime, for the full BFSS model with fermions the leading Lyapunov exponent, entanglement saturation time, and decay rate of quasinormal modes all remain finite and non-zero down to the lowest temperatures
Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
Using first-principle Hybrid-Monte-Carlo (HMC) simulations, we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in the extended Hubbard model on the two dimensional hexagonal lattice at half filling. We determine the phase diagram in the space of on-site and nearest-neighbor couplings and in the region , which can be simulated without a fermion sign problem, and find that a transition from semimetal to a SDW phase occurs at sufficiently large for basically all . Tracing the corresponding phase boundary from to the line, we find evidence for critical scaling in the Gross-Neveu universality class for the entire boundary. With rather high confidence we rule out the existence of the CDW ordered phase anywhere in the range of parameters considered. We also discuss several improvements of the HMC algorithm which are crucial to reach these conclusions, in particular the improved fermion action with exact sublattice symmetry and the complexification of the Hubbard-Stratonovich field to ensure the ergodicity of the algorithm
Some Field Theoretic Issues Regarding the Chiral Magnetic Effect
In this paper, we shall address some field theoretic issues regarding the
chiral magnetic effect. The general structure of the magnetic current
consistent with the electromagnetic gauge invariance is obtained and the impact
of the infrared divergence is examined. Some subtleties on the relation between
the chiral magnetic effect and the axial anomaly are clarified through a
careful examination of the infrared limit of the relevant thermal diagrams.Comment: 19 pages, 4 figures in Latex. Typos fixed, version accepted to be
published in JHE
Holographic Anomalous Conductivities and the Chiral Magnetic Effect
We calculate anomaly induced conductivities from a holographic gauge theory
model using Kubo formulas, making a clear conceptual distinction between
thermodynamic state variables such as chemical potentials and external
background fields. This allows us to pinpoint ambiguities in previous
holographic calculations of the chiral magnetic conductivity. We also calculate
the corresponding anomalous current three-point functions in special kinematic
regimes. We compare the holographic results to weak coupling calculations using
both dimensional regularization and cutoff regularization. In order to
reproduce the weak coupling results it is necessary to allow for singular
holographic gauge field configurations when a chiral chemical potential is
introduced for a chiral charge defined through a gauge invariant but
non-conserved chiral density. We argue that this is appropriate for actually
addressing charge separation due to the chiral magnetic effect.Comment: 17 pages, 1 figure. v2: 18 pages, 1 figure, discussion clarified
throughout the text, references added, version accepted for publication in
JHE
Chiral drag force
We provide a holographic evaluation of novel contributions to the drag force
acting on a heavy quark moving through strongly interacting plasma. The new
contributions are chiral in that they act in opposite directions in plasmas
containing an excess of left- or right-handed quarks and in that they are
proportional to the coefficient of the axial anomaly. These new contributions
to the drag force act either parallel to or antiparallel to an external
magnetic field or to the vorticity of the fluid plasma. In all these respects,
these contributions to the drag force felt by a heavy quark are analogous to
the chiral magnetic effect on light quarks. However, the new contribution to
the drag force is independent of the electric charge of the heavy quark and is
the same for heavy quarks and antiquarks. We show that although the chiral drag
force can be non-vanishing for heavy quarks that are at rest in the local fluid
rest frame, it does vanish for heavy quarks that are at rest in a suitably
chosen frame. In this frame, the heavy quark at rest sees counterpropagating
momentum and charge currents, both proportional to the axial anomaly
coefficient, but feels no drag force. This provides strong concrete evidence
for the absence of dissipation in chiral transport, something that has been
predicted previously via consideration of symmetries. Along the way to our
principal results, we provide a general calculation of the corrections to the
drag force due to the presence of gradients in the flowing fluid in the
presence of a nonzero chemical potential. We close with a consequence of our
result that is at least in principle observable in heavy ion collisions, namely
an anticorrelation between the direction of the CME current for light quarks in
a given event and the direction of the kick given to the momentum of all the
heavy quarks and antiquarks in that event.Comment: 28 pages, small improvement to the discussion of gravitational
anomaly, references adde
Chiral perturbation theory in a magnetic background - finite-temperature effects
We consider chiral perturbation theory for SU(2) at finite temperature in
a constant magnetic background . We compute the thermal mass of the pions
and the pion decay constant to leading order in chiral perturbation theory in
the presence of the magnetic field. The magnetic field gives rise to a
splitting between and as well as between
and . We also calculate the free energy and the
quark condensate to next-to-leading order in chiral perturbation theory. Both
the pion decay constants and the quark condensate are decreasing slower as a
function of temperature as compared to the case with vanishing magnetic field.
The latter result suggests that the critical temperature for the chiral
transition is larger in the presence of a constant magnetic field. The increase
of as a function of is in agreement with most model calculations but
in disagreement with recent lattice calculations.Comment: 24 pages and 9 fig
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