On boundary degrees of freedom in three dimensional Anti-de Sitter spacetime and thermofield-double

TL;DR

This paper explores two different representations of the thermofield-double state in three-dimensional Anti-de Sitter space, highlighting the role of boundary degrees of freedom and reparametrization modes in understanding entanglement.

Contribution

It introduces a novel perspective by relating the Kerr-BTZ black hole geometry to a disjoint union of circles governed by Schwarzian theory, emphasizing boundary modes.

Findings

Equivalence of the Kerr-BTZ and Schwarzian representations of TFD.

Reparametrization modes are crucial for understanding entanglement.

Boundary degrees of freedom influence the structure of TFD in AdS3.

Abstract

We will give two representations for thermofield-double (TFD). The first representation is the well-known Kerr-BTZ black hole geometry, which is the solution of Einstein's equation. The second representation is a disjoint union of two circles, which is a solution to two copies of the Schwarzian theory. This representation, in particular, admits the reparametrization modes, which are absent in any two dimensional CFT on a torus, and are essential for (dis-)entangling the TFD. Since the two representations describe the same state, they must be equivalent.