$W_{\infty} Algebra in Two-Dimensional Black Hole

TL;DR

This paper explores the algebraic structure of two-dimensional black holes, revealing their spectrum matches that of c=1 matter models and identifying key operators related to black hole mass.

Contribution

It uncovers an isomorphism between the algebraic structures of the black hole model and Liouville theory coupled to c=1 matter, highlighting their spectral equivalence.

Findings

Black hole model shares spectrum with c=1 matter, including tachyons and $W_$ currents.

Identifies the operator responsible for black hole mass creation.

Establishes an algebraic isomorphism between the models.

Abstract

We study the $SL(2;R)/U(1)$ coset model of two-dimensional black hole and its relation to the Liouville theory coupled to c=1 matter. We uncover a basic isomorphism in the algebraic structures of these theories and show that the black hole model has the same physical spectrum as the c=1 model, i.e. tachyons, $W_\infty$ currents and the ground ring elements. we also identify the operator responsible for the creation of the mass of the black hole.