Universality of Effective Central Charge in Interface CFTs

TL;DR

This paper investigates the universal properties of the effective central charge in interface conformal field theories, establishing bounds and proposing a higher-dimensional analogue with similar universal features.

Contribution

It clarifies the appearance of the effective central charge in general subsystems and introduces a universal upper bound, extending the concept to higher dimensions.

Findings

Universal upper bound on the effective central charge.

Effective central charge depends on interface transmissivity, not just central charges.

Proposal of a higher-dimensional analogue with similar universal properties.

Abstract

When an interface connects two CFTs, the entanglement entropy between the two CFTs is determined by a quantity called the effective central charge. The effective central charge does not have a simple form in terms of the central charges of the two CFTs, but intricately depends on the transmissive properties of the interface. In this article, we examine universal properties of the effective central charge. We first clarify how the effective central charge appears when considering general subsystems of the interface CFT. Then using this result and ideas used in the proof of the $c$-theorem, we provide a universal upper bound on the effective central charge. In past studies, the effective central charge was defined only in two dimensions. We propose an analogue of the effective central charge in general dimensions possessing similar universal properties as in two dimensions.