168 research outputs found
Phase Structure of Confining Theories on R^3 x S^1
Recent work on QCD-like theories on R^3 x S^1 has revealed that a confined
phase can exist when the circumference L of S^1 is sufficiently small. Adjoint
QCD and double-trace deformation theories with certain conditions are such
theories, and we present some new results for their phase diagrams. First we
show the connection between the large-L and small-L confined regions in the
phase diagram of SU(3) adjoint QCD using Polyakov-Nambu-Jona Lasinio models.
Then we consider an SU(2) double-trace deformation theory with adjoint scalars
and study conflicts between the Higgs and small-L confined phase.Comment: 3 pages, 2 figures. Talk given at the IX International Conference on
Quark Confinement and Hadron Spectrum - Madrid, Spain, 30 Aug 2010 - 03 Sep
201
Complex saddle points in QCD at finite temperature and density
The sign problem in QCD at finite temperature and density leads naturally to
the consideration of complex saddle points of the action or effective action.
The global symmetry of the finite-density action, where
is charge conjugation and is complex conjugation,
constrains the eigenvalues of the Polyakov loop operator at a saddle point
in such a way that the action is real at a saddle point, and net color charge
is zero. The values of and at the saddle point,
are real but not identical, indicating the different free energy cost
associated with inserting a heavy quark versus an antiquark into the system. At
such complex saddle points, the mass matrix associated with Polyakov loops may
have complex eigenvalues, reflecting oscillatory behavior in color-charge
densities. We illustrate these properties with a simple model which includes
the one-loop contribution of gluons and massless quarks moving in a constant
Polyakov loop background. Confinement-deconfinement effects are modeled
phenomenologically via an added potential term depending on the Polyakov loop
eigenvalues. For sufficiently large and , the results obtained reduce
to those of perturbation theory at the complex saddle point. These results may
be experimentally relevant for the CBM experiment at FAIR.Comment: 13 pages, 3 figures. Additional references and minor revision
Gradient flows without blow-up for Lefschetz thimbles
We propose new gradient flows that define Lefschetz thimbles and do not blow
up in a finite flow time. We study analytic properties of these gradient flows,
and confirm them by numerical tests in simple examples.Comment: 31 pages, 11 figures, (v2) conclusion part is expande
Possible higher order phase transition in large- gauge theory at finite temperature
We analyze the phase structure of gauge theory at finite
temperature using matrix models. Our basic assumption is that the effective
potential is dominated by double-trace terms for the Polyakov loops. As a
function of the temperature, a background field for the Polyakov loop, and a
quartic coupling, it exhibits a universal structure: in the large portion of
the parameter space, there is a continuous phase transition analogous to the
third-order phase transition of Gross, Witten and Wadia, but the order of phase
transition can be higher than third. We show that different confining
potentials give rise to drastically different behavior of the eigenvalue
density and the free energy. Therefore lattice simulations at large could
probe the order of phase transition and test our results.Comment: 7 pages, 2 figures, conference proceeding for Critical Point and
Onset of Deconfinement - CPOD201
PNJL model for adjoint fermions
Recent work on QCD-like theories has shown that the addition of adjoint
fermions obeying periodic boundary conditions to gauge theories on R^3 X S^1
can lead to a restoration of center symmetry and confinement for sufficiently
small circumference L of S^1. At small L, perturbation theory may be used
reliably to compute the effective potential for the Polyakov loop P in the
compact direction. Periodic adjoint fermions act in opposition to the gauge
fields, which by themselves would lead to a deconfined phase at small L. In
order for the fermionic effects to dominate gauge field effects in the
effective potential, the fermion mass must be sufficiently small. This
indicates that chiral symmetry breaking effects are potentially important. We
develop a Polyakov-Nambu-Jona Lasinio (PNJL) model which combines the known
perturbative behavior of adjoint QCD models at small L with chiral symmetry
breaking effects to produce an effective potential for the Polyakov loop P and
the chiral order parameter psi-bar psi. A rich phase structure emerges from the
effective potential. Our results are consistent with the recent lattice
simulations of Cossu and D'Elia, which found no evidence for a direct
connection between the small-L and large-L confining regions. Nevertheless, the
two confined regions are connected indirectly if an extended field theory model
with an irrelevant four-fermion interaction is considered. Thus the small-L and
large-L regions are part of a single confined phase.Comment: 6 pages, 4 figures; presented at INPC 201
Complex Saddle Points and Disorder Lines in QCD at finite temperature and density
The properties and consequences of complex saddle points are explored in
phenomenological models of QCD at non-zero temperature and density. Such saddle
points are a consequence of the sign problem, and should be considered in both
theoretical calculations and lattice simulations. Although saddle points in
finite-density QCD are typically in the complex plane, they are constrained by
a symmetry that simplifies analysis. We model the effective potential for
Polyakov loops using two different potential terms for confinement effects, and
consider three different cases for quarks: very heavy quarks, massless quarks
without modeling of chiral symmetry breaking effects, and light quarks with
both deconfinement and chiral symmetry restoration effects included in a pair
of PNJL models. In all cases, we find that a single dominant complex saddle
point is required for a consistent description of the model. This saddle point
is generally not far from the real axis; the most easily noticed effect is a
difference between the Polyakov loop expectation values and , and that is confined to small region in the plane. In all but one
case, a disorder line is found in the region of critical and/or crossover
behavior. The disorder line marks the boundary between exponential decay and
sinusoidally modulated exponential decay of correlation functions. Disorder
line effects are potentially observable in both simulation and experiment.
Precision simulations of QCD in the plane have the potential to clearly
discriminate between different models of confinement.Comment: 33 pages, 20 figure
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