The Algebra of Diffeomorphisms from the World Sheet

TL;DR

This paper explicitly derives the algebra of space-time diffeomorphisms in string theory using world sheet vertex operators, connecting it to double field theory and conformal field theory techniques.

Contribution

It provides a detailed realization of the diffeomorphism algebra in string theory and relates it to double field theory structures using vertex operators.

Findings

Explicit realization of diffeomorphism algebra in string theory.

Connection between world sheet vertex operators and space-time symmetries.

Identification of a left-right split related to the C-bracket.

Abstract

The quantum theory of a massless spin two particle is strongly constrained by diffeomorphism invariance, which is in turn implied by unitarity. We explicitly exhibit the space-time diffeomorphism algebra of string theory, realizing it in terms of world sheet vertex operators. Viewing diffeomorphisms as field redefinitions in the two-dimensional conformal field theory renders the calculation of their algebra straightforward. Next, we generalize the analysis to combinations of space-time anti-symmetric tensor gauge transformations and diffeomorphisms. We also point out a left-right split of the algebra combined with a twist that reproduces the C-bracket of double field theory. We further compare our derivation to an analysis in terms of marginal deformations as well as vertex operator algebras.