32 research outputs found
Confinement with Kalb - Ramond Fields
We consider models with N U(1) gauge fields A_{\mu}^n, N Kalb-Ramond fields
B_{\mu \nu}^n, an arbitrary bare action and a fixed UV cutoff \Lambda. Under
mild assumptions these can be obtained as effective low energy theories of
SU(N+1) Yang Mills theories in the maximal abelian gauge. For a large class of
bare actions they can be solved in the large N limit and exhibit confinement.
The confining phase is characterized by an approximate ``low energy'' vector
gauge symmetry under which the Kalb-Ramond fields B_{\mu\nu}^n transform. The
same symmetry allows for a duality transformation showing that magnetic
monopoles have condensed. The models allow for various mechanisms of
confinement, depending on which sources for A_{\mu}^n or B_{\mu \nu}^n are
switched on, but the area law for the Wilson loop is obtained in any case.Comment: corrected misprints and reference
Confinement and Mass Gap in Abelian Gauge
First, we present a simple confining abelian pure gauge theory. Classically,
its kinetic term is not positive definite, and it contains a simple UV
regularized F^4 interaction. This provoques the formation of a condensate ~ F^2
such that, at the saddle point of the effective potential, the wave function
normalization constant of the abelian gauge fields vanishes exactly. Then we
study SU(2) pure Yang-Mills theory in an abelian gauge and introduce an
additional auxiliary field for a BRST invariant condensate of dimension 2,
which renders the charged sector massive. Under simple assumptions its
effective low energy theory reduces to the confining abelian model discussed
before, and the vev of rho is seen to scale correctly with the renormalization
point. Under these assumptions, the confinement condition Z_eff = 0 also holds
for the massive charged sector, which suppresses the couplings of the charged
fields to the abelian gauge bosons in the infrared regime.Comment: Explanations added, to appear in Eur. Phys. J.
Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond
We study the confinement-deconfinement phase transition of pure Yang-Mills
theories at finite temperature using a simple massive extension of standard
background field methods. We generalize our recent next-to-leading-order
perturbative calculation of the Polyakov loop and of the related background
field effective potential for the SU(2) theory to any compact and connex Lie
group with a simple Lie algebra. We discuss in detail the SU(3) theory, where
the two-loop corrections yield improved values for the first-order transition
temperature as compared to the one-loop result. We also show that certain
one-loop artifacts of thermodynamical observables disappear at two-loop order,
as was already the case for the SU(2) theory. In particular, the entropy and
the pressure are positive for all temperatures. Finally, we discuss the groups
SU(4) and Sp(2) which shed interesting light, respectively, on the relation
between the (de)confinement of static matter sources in the various
representations of the gauge group and on the use of the background field
itself as an order parameter for confinement. In both cases, we obtain
first-order transitions, in agreement with lattice simulations and other
continuum approaches.Comment: 35 pages, 20 figure
Yang-Mills correlators at finite temperature: A perturbative perspective
We consider the two-point correlators of Yang-Mills theories at finite
temperature in the Landau gauge. We employ a model for the corresponding
Yang-Mills correlators based on the inclusion of an effective mass term for
gluons. The latter is expected to have its origin in the existence of Gribov
copies. One-loop calculations at zero temperature have been shown to agree
remarkably well with the corresponding lattice data. We extend on this and
perform a one-loop calculation of the Matsubara gluon and ghost two-point
correlators at finite temperature. We show that, as in the vacuum, an effective
gluon mass accurately captures the dominant infrared physics for the magnetic
gluon and ghost propagators. It also reproduces the gross qualitative features
of the electric gluon propagator. In particular, we find a slight nonmonotonous
behavior of the Debye mass as a function of temperature, however not as
pronounced as in existing lattice results. A more quantitative description of
the electric sector near the deconfinement phase transition certainly requires
another physical ingredient sensitive to the order parameter of the transition.Comment: 16 pages, 12 figures ; Published version (PRD
Deconfinement transition in SU(N) theories from perturbation theory
We consider a simple massive extension of the Landau-DeWitt gauge for SU()
Yang-Mills theory. We compute the corresponding one-loop effective potential
for a temporal background gluon field at finite temperature. At this order the
background field is simply related to the Polyakov loop, the order parameter of
the deconfinement transition. Our perturbative calculation correctly describes
a quark confining phase at low temperature and a phase transition of second
order for and weakly first order for . Our estimates for the
transition temperatures are in qualitative agreement with values from lattice
simulations or from other continuum approaches. Finally, we discuss the
effective gluon mass parameter in relation to the Gribov ambiguities of the
Landau-DeWitt gauge.Comment: 10 pages, 3 figure
Gauged supersymmetries in Yang-Mills theory
In this paper we show that Yang-Mills theory in the
Curci-Ferrari-Delbourgo-Jarvis gauge admits some up to now unknown local linear
Ward identities. These identities imply some non-renormalization theorems with
practical simplifications for perturbation theory. We show in particular that
all renormalization factors can be extracted from two-point functions. The Ward
identities are shown to be related to supergauge transformations in the
superfield formalism for Yang-Mills theory. The case of non-zero Curci-Ferrari
mass is also addressed.Comment: 11 pages. Minor changes. Some added reference
Superfluidity within Exact Renormalisation Group approach
The application of the exact renormalisation group to a many-fermion system
with a short-range attractive force is studied. We assume a simple ansatz for
the effective action with effective bosons, describing pairing effects and
derive a set of approximate flow equations for the effective coupling including
boson and fermionic fluctuations.
The phase transition to a phase with broken symmetry is found at a critical
value of the running scale. The mean-field results are recovered if boson-loop
effects are omitted. The calculations with two different forms of the regulator
was shown to lead to similar results.Comment: 17 pages, 3 figures, to appear in the proceedings of Renormalization
Group 2005 (RG 2005), Helsinki, Finland, 30 Aug - 3 Sep 200
Non Perturbative Renormalization Group, momentum dependence of -point functions and the transition temperature of the weakly interacting Bose gas
We propose a new approximation scheme to solve the Non Perturbative
Renormalization Group equations and obtain the full momentum dependence of
-point functions. This scheme involves an iteration procedure built on an
extension of the Local Potential Approximation commonly used within the Non
Perturbative Renormalization Group. Perturbative and scaling regimes are
accurately reproduced. The method is applied to the calculation of the shift
in the transition temperature of the weakly repulsive Bose gas, a
quantity which is very sensitive to all momenta intermediate between these two
regions. The leading order result is in agreement with lattice calculations,
albeit with a theoretical uncertainty of about 25%. The next-to-leading order
differs by about 10% from the best accepted result
Solutions of renormalization group flow equations with full momentum dependence
We demonstrate the power of a recently-proposed approximation scheme for the
non-perturbative renormalization group that gives access to correlation
functions over their full momentum range. We solve numerically the
leading-order flow equations obtained within this scheme, and compute the
two-point functions of the O(N) theories at criticality, in two and three
dimensions. Excellent results are obtained for both universal and non-universal
quantities at modest numerical cost.Comment: 4 pages, 1 figur
Non-Perturbative Renormalization Group calculation of the scalar self-energy
We present the first numerical application of a method that we have recently
proposed to solve the Non Perturbative Renormalization Group equations and
obtain the n-point functions for arbitrary external momenta. This method leads
to flow equations for the n-point functions which are also differential
equations with respect to a constant background field. This makes them, a
priori, difficult to solve. However, we demonstrate in this paper that, within
a simple approximation which turns out to be quite accurate, the solution of
these flow equations is not more complicated than that of the flow equations
obtained in the derivative expansion. Thus, with a numerical effort comparable
to that involved in the derivative expansion, we can get the full momentum
dependence of the n-point functions. The method is applied, in its leading
order, to the calculation of the self-energy in a 3-dimensional scalar field
theory, at criticality. Accurate results are obtained over the entire range of
momenta.Comment: 29 page