Non Abelian Toda Theory : A Completely Integrable Model for Strings on a Black Hole Background

Abstract

The present paper studies a completely integrable conformally invariant model in 1+1 dimensions that corresponds to string propagation on the two-dimensional black hole background (semi-ininite cigar). Besides the two space-time string fields there is a third (internal) field with a very specific Liouville-type interaction leading to the complete integrability. This system is known as non-abelian Toda theory. I give the general explicit classical solution. It realizes a rather involved transformation expressing the interacting string fields in terms of (three) functions ${\phi }_j(u)$ and ${\bar{\phi }}_j(v)$ of one light-cone variable only. The latter are shown to lead to standard harmonic oscillator (free field) Poisson brackets thus paving the way towards quantization. There are three left-moving and three right-moving conserved quantities. The right (left)-moving conserved quantities form a new closed non-linear, non-local Poisson bracket algebra. This algebra is a Virasoro algebra extended by two conformal dimension-two primaries.

41 pages, PUPT-1434

References in corpus (1)

• Black Holes from Non-Abelian Toda Theories

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