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($N$) 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 $N=2$ and weakly first order for $N=3$. 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 nn-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 $n$-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 $\Delta T_c$ 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