Embeddings of the Virasoro algebra and black hole entropy

TL;DR

This paper explores embeddings of the Virasoro algebra into larger algebras with different central charges, offering a novel approach to understanding black hole entropy in 2+1 dimensions.

Contribution

It introduces a new embedding method of the Virasoro algebra that could shed light on black hole entropy calculations.

Findings

Virasoro algebra with central charge c can embed into one with central charge 1.

This embedding provides a new perspective on the black hole entropy problem.

The approach links algebraic structures to gravitational entropy in lower dimensions.

Abstract

We consider embeddings of the Virasoro algebra into other Virasoro algebras with different central charges. A Virasoro algebra with central charge c (assumed to be a positive integer) and zero mode operator L_0 can be embedded into another Virasoro algebra with central charge one and zero mode operator c L_0. We point out that this provides a new route to investigate the black hole entropy problem in 2+1 dimensions.