The Roberge-Weiss transition for QCD in a magnetic background

TL;DR

This study explores how magnetic fields affect the Roberge-Weiss transition in QCD, revealing that magnetic fields lower the transition temperature and change the transition order from second to first, with implications for understanding QCD phase structure.

Contribution

It provides the first detailed numerical analysis of the impact of magnetic backgrounds on the RW transition in physical QCD, including the transition order change and critical magnetic field values.

Findings

Transition temperature decreases with magnetic field.

Transition changes from second to first order under strong magnetic fields.

Inverse magnetic catalysis observed above the transition.

Abstract

We investigate how a magnetic background field influences the location and the nature of the Roberge-Weiss (RW) finite temperature transition for $N_f = 2+1$ QCD with physical quark masses. To that purpose, we perform numerical simulations of the finite temperature theory, discretized through stout staggered quarks and the tree-level improved Symanzik pure gauge action, considering two different values of the Euclidean temporal extent in lattice units, $N_t = 6, 8$. The RW transition temperature $T_{RW}$ decreases with $eB$, in particular it follows closely the behavior of the pseudo-critical QCD crossover temperature $T_{pc}$, so that $T_{RW} (eB) - T_{pc}(eB)$ is practically constant, within errors, for magnetic fields up to $eB \sim 1$ GeV$^2$; consistent results are found from the drop of the chiral condensate, which signals chiral symmetry restoration, leading also to the phenomenon of inverse magnetic catalysis above the transition. Moreover, we find that the magnetic field turns the RW transition from second order to first order, with a tri-critical magnetic field in-between 1 and 2.4 GeV$^2$, i.e. for magnetic fields substantially lower than those for which the standard QCD transition turns to first order.