SciPost Phys. 19, 001 (2025) ·
published 1 July 2025
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We discuss the breakdown of the Parisi-Sourlas supersymmetry (SUSY) and of the dimensional-reduction (DR) property in the random field Ising and O($N$) models as a function of space dimension $d$ and/or number of components $N$. The functional renormalization group (FRG) predicts that this takes place below a critical line $d_\mathrm{DR}(N)$. We revisit the perturbative FRG results for the RFO($N$)M in $d=4+\epsilon$ and carry out a more comprehensive investigation of the nonperturbative FRG approximation for the RFIM. In light of this FRG description, we discuss the perturbative results in $\epsilon=6-d$ recently derived for the RFIM by Kaviraj, Rychkov, and Trevisani. We stress in particular that the disappearance of the SUSY/DR fixed point below $d_\mathrm{DR}$ arises as a consequence of the nonlinearity of the FRG equations and cannot be found via the perturbative expansion in $\epsilon=6-d$ (nor in $1/N$). We also provide an error bar on the value of the critical dimension $d_\mathrm{DR}$ for the RFIM, which we find around $5.11±0.09$, by studying several successive orders of the nonperturbative FRG approximation scheme.
Duifje Maria van Egmond, Urko Reinosa, Julien Serreau, Matthieu Tissier
SciPost Phys. 12, 087 (2022) ·
published 9 March 2022
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We propose a novel approach to the confinement-deconfinement transition in Yang-Mills theories in the context of gauge-fixed calculations. The method is based on a background-field generalisation of the Landau gauge (to which it reduces at vanishing temperature) with a given, center-symmetric background. This is to be contrasted with most implementations of background field methods in gauge theories, where one uses a variable, self-consistent background. Our proposal is a bona fide gauge fixing that can easily be implemented on the lattice and in continuum approaches. The resulting gauge-fixed action explicitly exhibits the center symmetry of the nonzero temperature theory that controls the confinement-deconfinement transition. We show that, in that gauge, the electric susceptibility diverges at a second order transition [e.g., in the SU(2) theory], so that the gluon propagator is a clear probe of the transition. We implement our proposal in the perturbative Curci-Ferrari model, known for its successful description of various infrared aspects of Yang-Mills theories, including the confinement-deconfinement transition. Our one-loop calculation confirms our general expectation for the susceptibility while providing transition temperatures in excellent agreement with the SU(2) and SU(3) lattice values. Finally, the Polyakov loops above the transition show a more moderate rise, in contrast to previous implementations of the Curci-Ferrari model using a self-consistent background, and our SU(3) result agrees quite well with lattice results in the range $[0,2T_c]$.
SciPost Phys. 10, 035 (2021) ·
published 16 February 2021
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We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.
