Universality of Abrupt Holographic Quenches

TL;DR

An analytic investigation of rapid quenches of relevant operators in d-dimensional holographic conformal field theories, which admit a dual gravity description, uncover a universal scaling behavior in the response of the system, which depends only on the conformal dimension of the quenched operator in the vicinity of the ultraviolet fixed point of the theory.

Abstract

We make an analytic investigation of rapid quenches of relevant operators in d-dimensional holographic CFT's, which admit a dual gravity description. We uncover a universal scaling behaviour in the response of the system, which depends only on the conformal dimension of the quenched operator in the vicinity of the ultraviolet fixed point of the theory. Unless the amplitude of the quench is scaled appropriately, the work done on a system during the quench diverges in the limit of abrupt quenches for operators with dimension $\frac{d}{2} \leΔ< d$.

Figures (4)

• Figure 1: (Colour online) The shaded triangle is the region close to the boundary of the AdS spacetime where we must solve for the scalar field. We show several cases with $\delta t_1<\delta t_2<\delta t_3$. The profile $\lambda(t/\delta t)$ is held fixed in each case. In particular, the amplitude $\delta\lambda$ of the quench remains constant as $\delta t$ becomes smaller. As the quench becomes more rapid, the bulk region shrinks closer to the asymptotic boundary.
• Figure 2: Normalized source $p_0/\delta p$ for eq. \ref{['sourcex']} as a function of the rescaled time $\hat{t}={t}/{\delta t}$.
• Figure 3: (Colour online) The response to the source \ref{['sourcex']} in $d=4$ for $\Delta=2.1$ through $2.9$ in steps of $0.1$. The plots with larger amplitudes correspond to larger $\Delta$.
• Figure 4: (Colour online) The response to the source \ref{['sourcex']} in $d=4$ for $\Delta=3.1$ through $3.4$ in steps of $0.1$. The colours blue, purple, orange, and red correspond to the response for $\Delta=3.1$ through $3.4$ respectively.