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

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.