Damián A. Galante — Page 2

arXiv2017

Shape Dependence of Holographic Rényi Entropy in General Dimensions

We present a holographic method for computing the response of Rényi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point function in a deformed hyperboloid background and relates it to the coefficient in the two-point function of the displacement operator. We obtain explicit numerical results for $d=3,\dots,6$ spacetime dimensions, and also evaluate analytically the limits where the Rényi index approaches 1 and 0 in general dimensions. We use our results to extend the work of 1602.08493 and disprove a set of conjectures in the literature regarding the relations between the Rényi shape dependence and the conformal weight of the twist operator. We also extend our analysis beyond leading order in derivatives in the bulk theory by studying Gauss-Bonnet gravity.

hep-th↗

arXiv2015

Smooth and fast versus instantaneous quenches in quantum field theory

We examine in detail the relationship between smooth fast quantum quenches, characterized by a time scale $δt$, and {\em instantaneous quenches}, within the framework of exactly solvable mass quenches in free scalar field theory. Our earlier studies \cite{dgm1,dgm2} highlighted that the two protocols remain distinct in the limit $δt \rightarrow 0$ because of the relation of the quench rate to the UV cut-off, i.e., $1/δt\llΛ$ always holds in the fast smooth quenches while $1/δt\simΛ$ for instantaneous quenches. Here we study UV finite quantities like correlators at finite spatial distances and the excess energy produced above the final ground state energy. We show that at late times and large distances (compared to the quench time scale) the smooth quench correlator approaches that for the instantaneous quench. At early times, we find that for small spatial separation and small $δt$, the correlator scales universally with $δt$, exactly as in the scaling of renormalized one point functions found in earlier work. At larger separation, the dependence on $δt$ drops out. The excess energy density is finite (for finite $mδt$) and scales in a universal fashion for all $d$. However, the scaling behaviour produces a divergent result in the limit $mδt \rightarrow 0$ for $d\ge4$, just as in an instantaneous quench, where it is UV divergent for $d \geq 4$. We argue that similar results hold for arbitrary interacting theories: the excess energy density produced is expected to diverge for scaling dimensions $Δ> d/2$.

hep-th↗