DeWitt-Virasoro construction

TL;DR

This paper develops a background-independent approach to analyze conformal invariance in bosonic string theory using DeWitt's quantum mechanics, constructing Virasoro generators that simplify in Ricci-flat backgrounds.

Contribution

It introduces DeWitt-Virasoro generators within a background-independent framework, extending the understanding of conformal invariance in curved string backgrounds.

Findings

DeWitt-Virasoro algebra is Witt with anomalous terms vanishing in Ricci-flat backgrounds.

Constructed background-independent Virasoro generators using DeWitt's formalism.

Demonstrated the approach in flat and pp-wave backgrounds.

Abstract

We study a particular approach for analyzing worldsheet conformal invariance for bosonic string propagating in a curved background using hamiltonian formalism. We work in the Schrodinger picture of a single particle description of the problem where the particle moves in an infinite-dimensional space. Background independence is maintained in this approach by adopting DeWitt's (Phys.Rev.85:653-661,1952) coordinate independent formulation of quantum mechanics. This enables us to construct certain background independent notion of Virasoro generators, called DeWitt-Virasoro (DWV) generators, and invariant matrix elements of an arbitrary operator constructed out of them in spin-zero representation. We show that the DWV algebra is given by the Witt algebra with additional anomalous terms that vanish for Ricci-flat backgrounds. The actual quantum Virasoro generators should be obtained by first introducing the vacuum state and then normal ordering the DWV generators with respect to that. We demonstrate the procedure in the simple cases of flat and pp-wave backgrounds. This is a shorter version of arXiv:0912.3987 [hep-th] with many technical derivations omitted.