All the entropies on the light-cone

TL;DR

This paper derives universal formulas for entanglement and Renyi entropies on the light-cone, showing they satisfy strong subadditivity and exhibit Markov properties, with implications for quantum field theories and holography.

Contribution

It provides explicit universal expressions for entropies on null surfaces and links them to anomaly actions, extending to holographic duals and quantum corrections.

Findings

Entropies saturate strong subadditivity.

Vacuum behaves like a product state (Markov property).

Universal logarithmic term from Wess-Zumino anomaly.

Abstract

We determine the explicit universal form of the entanglement and Renyi entropies, for regions with arbitrary boundary on a null plane or the light-cone. All the entropies are shown to saturate the strong subadditive inequality. This Renyi Markov property implies that the vacuum behaves like a product state. For the null plane, our analysis applies to general quantum field theories, while on the cone it is restricted to conformal field theories. In this case, the construction of the entropies is related to dilaton effective actions in two less dimensions. In particular, the universal logarithmic term in the entanglement entropy arises from a Wess-Zumino anomaly action. We also consider these properties in theories with holographic duals, for which we construct the minimal area surfaces for arbitrary shapes on the light-cone. We recover the Markov property and the universal form of the entropy, and argue that these properties continue to hold upon including stringy and quantum corrections. We end with some remarks on the recently proved entropic $a$-theorem in four spacetime dimensions.