arXiv subjects

David Vercauteren

Publications and source records attributed to David Vercauteren.

13 recordsLinked to original sources

arXiv2026

The Casimir effect in Gribov-Zwanziger theory

We consider Yang-Mills theory with two infinite parallel plates, separated by a distance $L$, that are perfect magnetic conductors (PMC) or perfect electric conductors (PEC). Recently, it was shown that the Gribov copy problem persists in such a setting. We then study the Gribov-Zwanziger (GZ) action in the presence of those boundaries using functional integral methods. Lagrange multiplier fields allow one to lift the boundary conditions into the action, after which the boundary modifications to the gluon propagator can straightforwardly be determined. In the PEC case, we provide evidence that, even when translation invariance is (partially) broken, the usual horizon term in the GZ action still restricts the functional integral to the Gribov region. We compute the Casimir energy for GZ with PMC or PEC plates, both directly from the functional integral and from the energy-momentum tensor, obtaining consistent results. We compare our analytical results with recent lattice data, in both 4D and 3D. A priori, one might expect that the boundary-modified gluon propagator introduces new $L$-dependencies into the GZ gap equation. This would make the Gribov mass $\gamma$ dynamically dependent on $L$, implying an interesting interplay with the Casimir energy. However, we show that no such dynamical $L$-dependence occurs within the current approximation.

hep-th↗

arXiv2026

Path-integral approach to Casimir effect with infinitely thin plates

When studying the Casimir effect in a quantum field theory setting, one can impose the boundary conditions by adding appropriate Dirac-delta functions to the path integral. In this paper, the limits of this approach are explored under different boundary conditions.

hep-th↗

arXiv2024

The Casimir energy with perfect electromagnetic boundary conditions and duality: a field-theoretic approach

Using functional integral methods, we study the Casimir effect for the case of two infinite parallel plates in the QED vacuum, with (different) perfect electromagnetic boundary conditions applied to both plates. To enforce these boundary conditions, we add two Lagrange multiplier fields to the action. We subsequently recover the known Casimir energy in two ways: once directly from the path integral, and once as the vacuum expectation value of the 00-component of the energy-momentum tensor. Comparing both methods, we show that the energy-momentum tensor must be modified, and that it picks up boundary contributions as a consequence. We also discuss electromagnetic duality-invariance of the theory and its interplay with the boundaries by generalizing the Deser-Teitelboim implementation of the duality transformation.

hep-th↗

arXiv2023

The gap equations of background field invariant Refined Gribov-Zwanziger action proposals and the deconfinement transition

In earlier work, we set up an effective potential approach at zero temperature for the Gribov-Zwanziger model that takes into account not only the restriction to the first Gribov region as a way to deal with the gauge fixing ambiguity, but also the effect of dynamical dimension-two vacuum condensates. Here, we investigate the model at finite temperature in presence of a background gauge field that allows access to the Polyakov loop expectation value and the Yang-Mills (de)confinement phase structure. This necessitates paying attention to BRST and background gauge invariance of the whole construct. We employ two such methods as proposed elsewhere in literature: one based on using an appropriate dressed, BRST invariant, gluon field by the authors and one based on a Wilson-loop dressed Gribov-Zwanziger auxiliary field sector by Kroff and Reinosa. The latter approach outperforms the former, in estimating the critical temperature for N=2, 3 as well as correctly predicting the order of the transition for both cases.

hep-th↗

arXiv2019

Gribov horizon, Polyakov loop and finite temperature

We consider finite-temperature $SU(2)$ gauge theory in the continuum formulation. Choosing the Landau gauge, the existing gauge copies are taken into account by means of the Gribov-Zwanziger quantization scheme, which entails the introduction of a dynamical mass scale (Gribov mass) directly influencing the Green functions of the theory. Here, we determine simultaneously the Polyakov loop (vacuum expectation value) and Gribov mass in terms of temperature, by minimizing the vacuum energy with respect to the Polyakov-loop parameter and solving the Gribov gap equation. The main result is that the Gribov mass directly feels the deconfinement transition, visible from a cusp occurring at the same temperature where the Polyakov loop becomes nonzero. Finally, problems for the pressure at low temperatures are reported.

hep-th↗

arXiv2018

BRST invariant $d=2$ condensates in Gribov-Zwanziger theory

In this proceeding, $SU(N)$ Yang-Mills theory is quantized in the linear covariant gauges, while taking into account the issue of Gribov copies and we construct the one-loop effective potential for a set of mass dimension 2 condensates, including the Gribov parameter, that refines the infrared region of the Gribov-Zwanziger theory, whilst respecting renormalization group invariance and BRST symmetry.

hep-ph↗

arXiv2014

Study of Yang-Mills-Chern-Simons theory in presence of the Gribov horizon

The two-point gauge correlation function in Yang--Mills--Chern--Simons theory in three dimensional Euclidean space is analysed by taking into account the non-perturbative effects of the Gribov horizon. In this way, we are able to describe the confinement and de-confinement regimes, which naturally depend on the topological mass and on the gauge coupling constant of the theory.

hep-th↗

arXiv2012

Schwinger-Dyson equations for gauge-invariant correlators

The formalism for Schwinger-Dyson equations of Wilson loops, as developed by Eguchi, Weingarten, and Foerster, is extended to include connected correlators. These should allow one to study propagators and interactions of glueball fields without having to handle gauge dependent fields such as gluons an ghosts. Some steps towards a solution are made.

hep-th↗

arXiv2011

The interplay between the condensate and instantons

Using the Local Composite Operator formalism, we analytically study the dimension two gluon condensate in the presence of instantons. We first use the dilute gas approximation and partially solve the infrared problem of instanton physics. In order to find quantitative results, however, we turn to an instanton liquid model, where we find a two-component picture of the condensate: one component comes from instantons, a second component is non-perturbatively generated by quantum fluctuations around the instantons.

hep-th↗

arXiv2011

A two-component picture of the condensate with instantons

We study the interplay between the condensate and instantons in non-Abelian gauge theory. Therefore we use the formalism of Local Composite Operators, with which the vacuum expectation value of this condensate can be analytically computed. We first use the dilute gas approximation and partially solve the infrared problem of instanton physics. In order to find quantitative results, however, we turn to an instanton liquid model, where we find how the different contributions to the condensate add up.

hep-th↗

arXiv2010

Analytic approach to the study of the electric-magnetic asymmetry of the dimension 2 condensate

Recent work by Chernodub and Ilgenfritz has uncovered non-trivial temperature dependence in the electric-magnetic asymmetry in the dimension 2 condensate. This asymmetry measures the difference between the spatial and the temporal components of the condensate. Lattice computations have shown very interesting phenomena. The asymmetry shows a jump at the deconfinement phase transition, beyond which it approaches its perturbative value. At temperatures lower than the critical temperature, it shows an exponential behavior with in the exponent a mass smaller than the lowest glueball mass. In this talk we present research done on this asymmetry, using a generalization of analytical methods developed to study . The purpose is to shed more insight on the findings of Chernodub and Ilgenfritz.

hep-th↗

arXiv2010

The asymmetry of the dimension two condensate

I present recent analytical work concerning the electric-magnetic asymmetry in the dimension two condensate in pure Yang-Mills theory. We reproduce qualitatively the lattice results previously found by Chernodub and Ilgenfritz.

hep-th↗

arXiv2007

Resolving the instability of the Savvidy vacuum by dynamical gluon mass

In this paper we apply the formalism of local composite operators as developed by Verschelde et al. in combination with a constant chromomagnetic field as considered in the seventies by Savvidy and others. We find that a nonzero minimizes the vacuum energy, as in the case with no chromomagnetic field, and that the chromomagnetic field itself is near-to zero. The Nielsen-Olesen instability, caused by the imaginary part in the action, also vanishes. We further investigate the effect of an external chromomagnetic field on the value of , finding that this condensate is destroyed by sufficiently strong fields. The inverse scenario, where is considered as external, results in analogous findings: when this condensate is sufficiently large, the induced chromomagnetic field is lowered to a perturbative value slightly below the applied .

hep-th↗