Abstract. We study a gauge invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang-Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson-Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.
Within the two-dimensional repulsive t −t ′ -Hubbard model, an attractive coupling in the d-wave pairing channel is induced by antiferromagnetic fluctuations. We investigate this coupling using functional renormalization group equations. The momentum dependent d-wave coupling can be bosonized by the use of scale dependent field transformations. We propose an effective coarse grained model for the Hubbard model which is based on the exchange of antiferromagnetic and d-wave collective bosons.
We examine the Nambu -Jona-Lasinio model in its SU(2) form, and coxnpare this with chiral perturbation theory (CPT). We use a consistent Hartree approximation as being the leading term in a liN, expansion for our mean field calculations and we make implicit chiral expansions of all the physical quantities directly from their defining equations. This enables us to extract explicit expressions for the observable scale-independent constants that are used in CPT. We find that this procedure gives reasonable agreement for the scale-independent constants. We compare our results with existing direct calculations in the literature, and point out difficulties in interpretation, especially with regard to L5 and lz. Our results appear to be in line with the agreement obtained via methods of bosonization, although, due to the diff'erent approximations made, these methods are not directly comparable. PACS number(s): 24.85. +p, 12.39.Fe, 12.60.Rc perconductivity, with particle-antiparticle binding playing the role of the Cooper pair. The connection of the N JL model to mesonic theories can thus be made by constructing a Ginzburg-Landau-like equation directly from it [8], and this simply gives rise to the linear sigma model under certain approximations [9].The question that arises now is how well this model agrees with chiral perturbation theory. This question has already been. examined by several authors over the last few years [10 -16] in both its two and three flavor versions, and thus we first give a brief overview of the literature. Unfortunately, results reported have been somewhat conflicting. In a direct calculation of the pion mass M and decay constant F" in a two flavor model in Ref. [11], the authors use an O(3) and O(4) regulator, and extract values for two of these constants, l3 and l4, that underestimate the CPT values by more than a factor of 3, and they thus draw a negative conclusion. A further calculation in Ref.[16] reexamines the problem for an O(4) regulator, and finds, however, that l3 and l4 can be reasonably well reproduced. The parameter set that these authors use differs &om that in Ref. [11], and they conclude that a lower constituent quark mass, of the order of 250 MeV, is required for a reasonable agreement. Both sets of authors make use of the so-called mean field approxima-
We investigate the chiral phase transition at finite temperatures and zero chemical potential with Dyson-Schwinger equations. Our truncation for the quark-gluon interaction includes mesonic degrees of freedom, which allows us to study the impact of the pions on the nature of the phase transition. Within the present scheme we find a five percent change of the critical temperature due to the pion backreaction whereas the mean field character of the transition is not changed.We investigate the chiral transition of two flavor QCD in the chiral limit (i.e. massless quarks). Assuming that effective restoration of axial vector symmetry takes place at temperatures above the critical temperature of chiral symmetry restoration the transition is expected to be a second order phase transition falling in the O(4)-universality class [1]. This motivates the application of effective models constructed in terms of order parameters to describe chiral transitions, see e.g. [1, 2] and references therein. Explicit symmetry breaking changes the second order transition to a smooth crossover.Here we study the chiral symmetry restoration with Dyson-Schwinger equations (DSE). In order to take into account the relevant degrees of freedom, i.e. the ones which retain long-range fluctuations in the vicinity of a second order phase transition, we need to employ a truncation of the quark-gluon vertex that includes mesonic fluctuations. Such a scheme has been proposed in [3]. At finite temperatures it leads to a renormalised quark DSE of the formis the inverse dressed quark propagator with dressing functions A, B, C and S −1 0 its bare counterpart. Z 2 and Z 1F are renormalisation constants and ω n = πT (2n + 1) is the fermion Matsubara frequency. In the quark self energy we have the dressed gluon propagator D νµ and the quark-gluon vertex Γ ν . The truncation of the quark-gluon vertex together with the resulting form of the quark-DSE is given diagrammatically in Fig.1. The symbol 'YM' denotes contributions from the gluonic sector of QCD whereas the meson exchange diagram contains in principle all possible mesonic fluctuations, see [3] for details. As a first step towards a more complete description, the preliminary results reported here include only pion contributions on a qualitative level. *
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