Thermal quenches in N=2* plasmas

TL;DR

This study uses gauge/gravity duality to analyze thermal quenches in the strongly coupled ${ m N}=2^{*}$ plasma, implemented by time-dependent bosonic and fermionic masses in the high-temperature, perturbative regime ${m}/{T}\ll1$. The authors develop a holographic renormalization framework for time-varying couplings and identify a dimensionless quench rate $m{ mamilyalpha}=rac{ mamilypi T_i}{1} mamilycal T$ that differentiates fast and slow quenches. They find that fast quenches relax via the lowest bulk-scalar quasinormal mode, while slow quenches proceed nearly adiabatically with entropy production controlled by a boundary-operator dependent coefficient $a_{2,4}^ ext{infty}$ (or its reverse-quench counterpart), revealing universal scaling and explicit scheme ambiguities. Their results illuminate how strongly coupled plasmas respond to rapid external perturbations and underscore the role of renormalization ambiguities in time-dependent holographic settings, pointing to future nonlinear and nonlocal investigations. Overall, the work provides a framework for understanding nonequilibrium dynamics in holographic gauge theories under temporally varying couplings and highlights observable signatures tied to quench rate and operator content.

Abstract

We exploit gauge/gravity duality to study `thermal quenches' in a plasma of the strongly coupled N=2* gauge theory. Specifically, we consider the response of an initial thermal equilibrium state of the theory under variations of the bosonic or fermionic mass, to leading order in m/T<<1. When the masses are made to vary in time, novel new counterterms must be introduced to renormalize the boundary theory. We consider transitions the conformal super-Yang-Mills theory to the mass deformed gauge theory and also the reverse transitions. By construction, these transitions are controlled by a characteristic time scale \calt and we show how the response of the system depends on the ratio of this time scale to the thermal time scale 1/T. The response shows interesting scaling behaviour both in the limit of fast quenches with T\calt<<1 and slow quenches with T\calt>>1. In the limit that T\calt\to\infty, we observe the expected adiabatic response. For fast quenches, the relaxation to the final equilibrium is controlled by the lowest quasinormal mode of the bulk scalar dual to the quenched operator. For slow quenches, the system relaxes with a (nearly) adiabatic response that is governed entirely by the late time profile of the mass. We describe new renormalization scheme ambiguities in defining gauge invariant observables for the theory with time dependant couplings.

Figures (17)

• Figure 1: (Colour online) Evolution of the normalizable component $p_{1,2}$ (left panel) and $p_{1,0}$ (right panel) during the quenches in eqs. \ref{['mq3']} and \ref{['mq2']}, respectively, with $\alpha=1$. The dashed red lines represent the adiabatic response given by eqs. \ref{['adresponse']} and \ref{['adresponsedim2']}, respectively.
• Figure 2: (Colour online) The curves on the left plot represent the evolution of the $\alpha$-rescaled normalizable component, $\alpha^2\ p_{1,2}$, as a function of $\frac{\tau}{\alpha}$ during the quench \ref{['mq3']} with different values of $\alpha$. The curves on the right plot represent the evolution of the normalizable component, $p_{1,2}$, as a function of $\frac{\tau}{\alpha}$ during the quench \ref{['mq3']} for the representative values of $\alpha$.
• Figure 3: (Colour online) ${\cal F}(\alpha)$ quantifies the response $p_{1,2}$ for abrupt quenches, i.e., as $\alpha\to 0$ --- see the definition in eq. \ref{['deff']}. The blue dots correspond to ${\cal F}(\alpha_n)$ for $\alpha_n=2^{-n}$ with $n=5,\ldots,11$. The dashed red line represents the linear fit to these points given in eq. \ref{['fitfa']}.
• Figure 4: (Colour online) Universality of the subtracted response $\hat{p}_{1,2}$ (defined in eq. \ref{['p12s']}) for abrupt quenches. The different curves are virtually indistinguishable from each other.
• Figure 5: (Colour online) Log-log plot of coefficient $(-a_{2,4}^\infty)$ as a function of $\alpha$. The dashed red lines represent the linear fits to the data (blue curve) for 'fast' quenches with small $\alpha$ ($\ln\alpha \to -\infty$) and for 'slow' quenches with large $\alpha$ ($\ln\alpha \to +\infty$). The dashed green and orange horizontal lines indicate the thresholds given in eqs. \ref{['largeenergy']} and \ref{['larget']}, respectively. For values of $(-a_{2,4}^\infty)$ above the dashed green line, both classes of quenches produce a final energy density which exceeds the initial energy density. For values of $(-a_{2,4}^\infty)$ above dashed orange line, the final temperature is always larger than the initial temperature for either type of quench. See the discussion in the main text.