Minimal Landau background gauge on the lattice

Abstract

We present the first numerical implementation of the minimal Landau background gauge for Yang-Mills theory on the lattice. Our approach is a simple generalization of the usual minimal Landau gauge and is formulated for general SU(N) gauge group. We also report on preliminary tests of the method in the four-dimensional SU(2) case, using different background fields. Our tests show that the convergence of the numerical minimization process is comparable to the case of a null background. The uniqueness of the minimizing functional employed is briefly discussed.In Ref.[1] Cornwall pleaded with the lattice community for an answer to the following question: Can you find a way of doing lattice simulations in the backgroundfield Feynman gauge? The reason for this request is that one can show [2] -to all orders in perturbation theory -that there is a simple correspondence between the background-field method in the Feynman gauge [3] and the so-called pinch technique [4], which allows one to build gauge-invariant off-shell Green functions in the continuum.Let us note that the numerical implementation of Landau gauge fixing (e.g. for the evaluation of Green functions) is well understood [5]. Recently, it has been shown that practical simulations of the linear covariant gauge are also possible [6] and that, with a suitable discretization of the gluon field, it becomes feasible to treat the Feynman gauge [7]. Here we present the first numerical implementation of the minimal Landau background gauge on the lattice. Our proposal is based on Ref. [8], which considers this gauge in the continuum.The covariant background gauge condition is introduced [9] by splitting the (continuum) Yang-Mills field A µ (x) into a quantum fluctuation component Q µ (x) and a background field B µ (x), i.e.

Deconfinement transition in SU( N ) theories from perturbation theory

“…Indeed, it is well-known that the Landau gauge condition can be obtained by extremizing the functional x tr{ A U μ A U μ } with respect to U for a given A, which is the basis of efficient numerical implementations in lattice calculations. A simple generalization to the LDW gauge reads [48] FĀ [a, U ] = x tr a U μ a U μ . (45) It is easy to check that the extrema of this functional with respect to U for fixed a and Ā satisfy the LDW condition (2).…”

Gluon propagator in two-color dense QCD: Massive Yang-Mills approach at one loop

“…We combine the in-medium effects with non-perturbative vacuum gluon propagators. For the latter, the Landau gauge studies in lattice QCD [27,28] and functional approaches [29][30][31][32] for pure Yang Mills (YM) theory have reported the generation of effective mass of m g ∼ 0.4-0.7 GeV at soft Euclidean momenta (see Refs. [33][34][35] for early studies).…”

Extracting topological information from momentum space propagators

“…For future work, it would be interesting to use improved fits to more recent finite temperature gluon data, to see if the phase transition coincides with the deconfinement transition. That such is possible can be inferred from the preliminary fitting report of [40], where in contrast to the here used numbers of [39], there are complex poles below (up to T = 0) and around T c . More takes on the analytic structure of gluon and/or quark propagators can be found in e.g.…”

“…In order to explicitly show that our generalized topological object (10) can in fact be applied to the topological analysis of bosonic relativistic quantum fields within the MST framework, we perform here the topological classification of the space defined by the two-point Green function of gluons, whose analytic expression is one that has been used in literature to fit lattice data at zero and finite temperature, according to [13,19,39,40]. Such analytic expression can be derived by means of the Refined Gribov-Zwanziger framework, see e.g.…”