Chiral symmetry breaking in accelerating and rotating frames

TL;DR

The paper tackles how acceleration and rotation affect chiral symmetry in QCD-like matter using low-energy effective models in non-inertial frames. It develops a formalism in Rindler coordinates, derives gap equations for NLσM and NJL models, and reveals a critical role for the renormalization scheme: subtracting Rindler vacuum leads to an acceleration-independent $T_c$ determined by the local Tolman-like temperature, while subtracting Minkowski vacuum yields acceleration-enhanced symmetry breaking. Extending to combined acceleration and rotation, the work identifies two restoration mechanisms—acceleration-induced thermalization and rotation-induced chemical potential effects—and shows the critical acceleration $a_c$ decreases with angular velocity $Ω$, with stronger rotation effects at larger radii. These findings illuminate the interplay between Unruh-like thermality and rotation in QCD-like matter and highlight foundational questions about vacuum interpretation in non-inertial settings.

Abstract

We study chiral symmetry breaking and restoration in accelerating and rotating frames using low-energy effective models. By analyzing the chiral condensate in Rindler coordinates, we show that different renormalization schemes lead to distinct conclusions in accelerating frame: the scheme with subtracting divergences in Rindler vacuum supports an acceleration-independent critical temperatures, while the other scheme with subtracting divergences in Minkowski vacuum suggests enhanced critical temperature. We further investigate system with both rotation and acceleration. We find that the critical acceleration (see definition in Section V) for chiral symmetry restoration decreases with angular velocity, indicating cooperative effects from acceleration-induced thermalization and rotation-induced effective chemical potential.

Figures (6)

• Figure 1: The $T-a$ phase diagram based on Eq. (\ref{['eq:Tcboson']})(for bosons) and Eq. (\ref{['eq:Tcferimion']})(for fermions). $T_{c0}$ denotes the critical the critical temperature in $a=0$. Blue region denotes the chiral symmetry breaking phase, while the white region denotes the chiral symmetry restored phase. Grey region denotes area of $T<T_U$ which is not explored in this study.
• Figure 2: The $T-a$ phase diagram calculated from Eq. (\ref{['eq.tce']}) and Eq. (\ref{['anotherfermion']}).
• Figure 3: The constituent quark mass as a function of acceleration $a$ with $T=T_U$ at different $\Omega$, calculated from Eq. (\ref{['eq:gapm=0']}).
• Figure 4: The constituent quark mass as a function of $\Omega$ for different acceleration $a$ with $T=T_U$, calculated from Eq. (\ref{['eq:gapm=0']}).
• Figure 5: Critical acceleration $a_c$ as a function of $\Omega$ at $r=0$ and $T=T_U$ calculated from numerical solving Eq. (\ref{['eq:gapm=0']}) and analytical equation Eq. (\ref{['eq:analyticalgap']}). The results of both are consistent with each other.