Conformal perturbation theory confronts lattice results in the vicinity of a critical point

Marcello Scanavino,Marco Panero,Michele Caselle,Nicodemo Magnoli,Alessandro Nada

doi:10.1103/physrevd.100.034512

Abstract

We study the accuracy and predictive power of conformal perturbation theory by a comparison with lattice results in the neighborhood of the finite-temperature deconfinement transition of SU(2) Yang-Mills theory, assuming that the infrared properties of this non-Abelian gauge theory near criticality can be described by the Ising model. The results of this comparison show that conformal perturbation theory yields quantitatively accurate predictions in a broad temperature range. We discuss the implications of these findings for the description of the critical point (belonging to the same universality class) of another strongly coupled, non-supersymmetric non-Abelian gauge theory: the critical end-point in the phase diagram of QCD at finite temperature and finite quark chemical potential.

Highlights

Since the publication of a seminal article by Zamolodchikov [1], conformal perturbation theory (CPT) has proved a powerful analytical tool to describe statisticalmechanics models and quantum field theories in the vicinity of a critical point
We propose to use CPT to study the behavior of quantum chromodynamics (QCD) and other strongly coupled non-Abelian gauge theories near the critical points associated with a continuous phase transition in their phase diagram
We argue that conformal perturbation theory could allow one to study the physics of strongly coupled QCD matter at values of temperature and net baryonic density lying along the “trajectories” scanned in experiments, as long as such trajectories pass sufficiently close to the critical point

Summary

INTRODUCTION

Since the publication of a seminal article by Zamolodchikov [1], conformal perturbation theory (CPT) has proved a powerful analytical tool to describe statisticalmechanics models and quantum field theories in the vicinity of a critical point. It is important to understand how well conformal perturbation theory works at a quantitative level, i.e., how large is the range of parameters of the underlying microscopic theory (in this case, QCD), for which the resulting low-energy physics can be approximated well by the associated conformal model (in this case, the Ising model in three dimensions) at or near criticality To this purpose, in this work we present a detailed comparison of theoretical predictions from conformal perturbation theory with those derived numerically using lattice simulations. In this work we present a detailed comparison of theoretical predictions from conformal perturbation theory with those derived numerically using lattice simulations We do this for SU(2) Yang-Mills theory, a strongly coupled non-Abelian gauge theory in four spacetime dimensions exhibiting a continuous phase transition at a finite deconfinement temperature Tc, which is in the same universality class [23] as the one associated with the critical end point of QCD, namely the one of the Ising model in three dimensions. Preliminary results of this work have been reported in Ref. [37]

CONFORMAL PERTURBATION THEORY

Setup of the lattice calculation

Comparison with CPT predictions

Systematic uncertainties