23 research outputs found
Induced Universal Properties and Deconfinement
We propose a general strategy to determine universal properties induced by a
nearby phase transition on a non-order parameter field. A general
renormalizable Lagrangian is used, which contains the order parameter and a
non-order parameter field, and respects all the symmetries present. We
investigate the case in which the order parameter field depends only on space
coordinates and the case in which this field is also time dependent. We find
that the spatial correlators of the non-order parameter field, in both cases,
are infrared dominated and can be used to determine properties of the phase
transition. We predict a universal behavior for the screening mass of a generic
singlet field, and show how to extract relevant information from such a
quantity. We also demonstrate that the pole mass of the non-order parameter
field is not infrared sensitive. Our results can be applied to any continuous
phase transition. As an example we consider the deconfining transition in pure
Yang-Mills theory, and show that our findings are supported by lattice data.
Our analysis suggests that monitoring the spatial correlators of different
hadron species, more specifically the derivatives of these, provides an
efficient and sufficient way to experimentally uncover the deconfining phase
transition and its features.Comment: Added computational details and improved the text. The results are
unchange
The Finite Temperature SU(2) Savvidy Model with a Non-trivial Polyakov Loop
We calculate the complete one-loop effective potential for SU(2) gauge bosons
at temperature T as a function of two variables: phi, the angle associated with
a non-trivial Polyakov loop, and H, a constant background chromomagnetic field.
Using techniques broadly applicable to finite temperature field theories, we
develop both low and high temperature expansions. At low temperatures, the real
part of the effective potential V_R indicates a rich phase structure, with a
discontinuous alternation between confined (phi=pi) and deconfined phases
(phi=0). The background field H moves slowly upward from its zero-temperature
value as T increases, in such a way that sqrt(gH)/(pi T) is approximately an
integer. Beyond a certain temperature on the order of sqrt(gH), the deconfined
phase is always preferred. At high temperatures, where asymptotic freedom
applies, the deconfined phase phi=0 is always preferred, and sqrt(gH) is of
order g^2(T)T. The imaginary part of the effective potential is non-zero at the
global minimum of V_R for all temperatures. A non-perturbative magnetic
screening mass of the form M_m = cg^2(T)T with a sufficiently large coefficient
c removes this instability at high temperature, leading to a stable
high-temperature phase with phi=0 and H=0, characteristic of a
weakly-interacting gas of gauge particles. The value of M_m obtained is
comparable with lattice estimates.Comment: 28 pages, 5 eps figures; RevTeX 3 with graphic
PT Symmetry and QCD: Finite Temperature and Density
The relevance of PT symmetry to quantum chromodynamics (QCD), the gauge theory of the strong interactions, is explored in the context of finite temperature and density. Two significant problems in QCD are studied: the sign problem of finite-density QCD, and the problem of confinement. It is proven that the effective action for heavy quarks at finite density is PT-symmetric. For the case of 1+1 dimensions, the PT-symmetric Hamiltonian, although not Hermitian, has real eigenvalues for a range of values of the chemical potential μ, solving the sign problem for this model. The effective action for heavy quarks is part of a potentially large class of generalized sine-Gordon models which are non-Hermitian but are PT-symmetric. Generalized sine-Gordon models also occur naturally in gauge theories in which magnetic monopoles lead to confinement. We explore gauge theories where monopoles cause confinement at arbitrarily high temperatures. Several different classes of monopole gases exist, with each class leading to different string tension scaling laws. For one class of monopole gas models, the PT-symmetric affine Toda field theory emerges naturally as the effective theory. This in turn leads to sine-law scaling for string tensions, a behavior consistent with lattice simulations
Thermodynamics of the PNJL model
QCD thermodynamics is investigated by means of the Polyakov-loop-extended
Nambu Jona-Lasinio (PNJL) model, in which quarks couple simultaneously to the
chiral condensate and to a background temporal gauge field representing
Polyakov loop dynamics. The behaviour of the Polyakov loop as a function of
temperature is obtained by minimizing the thermodynamic potential of the
system. A Taylor series expansion of the pressure is performed. Pressure
difference and quark number density are then evaluated up to sixth order in
quark chemical potential, and compared to the corresponding lattice data. The
validity of the Taylor expansion is discussed within our model, through a
comparison between the full results and the truncated ones.Comment: 6 pages, 5 figures, Talk given at the Workshop for Young Scientists
on the Physics of Ultrarelativistic Nucleus-Nucleus Collisions (Hot Quarks
2006), Villasimius, Italy, 15-20 May 200
Two-point functions for SU(3) Polyakov Loops near T_c
We discuss the behavior of two point functions for Polyakov loops in a SU(3)
gauge theory about the critical temperature, T_c. From a Z(3) model, in mean
field theory we obtain a prediction for the ratio of masses at T_c, extracted
from correlation functions for the imaginary and real parts of the Polyakov
loop. This ratio is m_i/m_r = 3 if the potential only includes terms up to
quartic order in the Polyakov loop; its value changes as pentic and hexatic
interactions become important. The Polyakov Loop Model then predicts how
m_i/m_r changes above T_c.Comment: 5 pages, no figures; reference adde
Polyakov Loops versus Hadronic States
The order parameter for the pure Yang-Mills phase transition is the Polyakov
loop which encodes the symmetries of the Z_N center of the SU(N) gauge group.
On the other side the physical degrees of freedom of any asymptotically free
gauge theory are hadronic states. Using the Yang-Mills trace anomaly and the
exact Z_N symmetry we construct a model able to communicate to the hadrons the
information carried by the order parameter.Comment: RevTex4 2-col., 6 pages, 2 figures. Typos fixed and added a paragraph
in the conclusion
Partial Deconfinement in Color Superconductivity
We analyze the fate of the unbroken SU(2) color gauge interactions for 2
light flavors color superconductivity at non zero temperature. Using a simple
model we compute the deconfining/confining critical temperature and show that
is smaller than the critical temperature for the onset of the superconductive
state itself. The breaking of Lorentz invariance, induced already at zero
temperature by the quark chemical potential, is shown to heavily affect the
value of the critical temperature and all of the relevant features related to
the deconfining transition. Modifying the Polyakov loop model to describe the
SU(2) immersed in the diquark medium we argue that the deconfinement transition
is second order. Having constructed part of the equation of state for the 2
color superconducting phase at low temperatures our results are relevant for
the physics of compact objects featuring a two flavor color superconductive
state.Comment: 9 pp, 4 eps-figs, version to appear in PR
Conformality or confinement: (IR)relevance of topological excitations
We study aspects of the conformality to confinement transition for
non-supersymmetric Yang-Mills theories with fermions in arbitrary chiral or
vectorlike representations. We use the presence or absence of mass gap for
gauge fluctuations as an identifier of the infrared behavior. Present-day
understanding does not allow the mass gap for gauge fluctuations to be computed
on R*4. However, recent progress allows its non-perturbative computation on
R*3xS*1 by using either the twisted partition function or deformation theory,
for a range of S*1 sizes depending on the theory. For small number of fermions,
Nf, we show that the mass gap increases with increasing radius, due to the
non-dilution of monopoles and bions, the topological excitations relevant for
confinement on R*3xS*1. For sufficiently large Nf, we show that the mass gap
decreases with increasing radius. In a class of theories, we claim that the
decompactification limit can be taken while remaining within the region of
validity of semi-classical techniques, giving the first examples of
semiclassically solvable Yang-Mills theories at any size S*1. For general
non-supersymmetric vectorlike or chiral theories, we conjecture that the change
in the behavior of the mass gap on R*3xS*1 as a function of the radius occurs
near the lower boundary of the conformal window and give non-perturbative
estimates of its value. For vectorlike theories, we compare our estimates of
the conformal window with existing lattice results, truncations of the
Schwinger-Dyson equations, NSVZ beta function-inspired estimates, and degree of
freedom counting criteria. For multi-generation chiral gauge theories, to the
best of our knowledge, our estimates of the conformal window are the only known
ones.Comment: 40 pages, 3 figures; modified various comments, reference adde
Chiral symmetry restoration and the Z3 sectors of QCD
Quenched SU(3) lattice gauge theory shows three phase transitions, namely the
chiral, the deconfinement and the Z3 phase transition. Knowing whether or not
the chiral and the deconfinement phase transition occur at the same temperature
for all Z3 sectors could be crucial to understand the underlying microscopic
dynamics. We use the existence of a gap in the Dirac spectrum as an order
parameter for the restoration of chiral symmetry. We find that the spectral gap
opens up at the same critical temperature in all Z3 sectors in contrast to
earlier claims in the literature.Comment: 4 pages, 4 figure
Trace Anomaly and Quasi-Particles in Finite Temperature SU(N) Gauge Theory
We consider deconfined matter in SU(N) gauge theory as an ideal gas of
transversely polarized quasi-particle modes having a temperature-dependent mass
m(T). Just above the transition temperature, the mass is assumed to be
determined by the critical behavior of the energy density and the screening
length in the medium. At high temperature, it becomes proportional to T as the
only remaining scale. The resulting (trace anomaly based) interaction measure
Delta=(e - 3P)/T^4 and energy density are found to agree well with finite
temperature SU(3) lattice calculations.Comment: 13 pages, 13 figures; references added for version