Extended First Law for Entanglement Entropy in Lovelock Gravity

Abstract

The first law for the holographic entanglement entropy of spheres in a boundary CFT with a bulk Lovelock dual is extended to include variations of the bulk Lovelock coupling constants. Such variations in the bulk correspond to perturbations within a family of boundary CFTs. The new contribution to the first law is found to be the product of the variation $\delta a$ of the A-type trace anomaly coefficient for even dimensional CFTs, or more generally its extension $\delta a^{\ast }$ to include odd dimensional boundaries, times the ratio $S/a^{\ast }$. Since $a^{\ast }$ is a measure of the number of degrees of freedom $N$ per unit volume of the boundary CFT, this new term has the form $\mu \delta N$, where the chemical potential $\mu$ is given by the entanglement entropy per degree of freedom.

18 pages

References in corpus (9)

• Holographic c-theorems in arbitrary dimensions
• Viscosity Bound and Causality Violation
• Seeing a c-theorem with holography
• Entanglement entropy, conformal invariance and extrinsic geometry
• Thermodynamical Property of Entanglement Entropy for Excited States
• Smarr Formula and an Extended First Law for Lovelock Gravity
• Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
• The holographic entropy increases in quadratic curvature gravity
• Entropy functionals and c-theorems from the second law