The Algebra of Diffeomorphisms from the World Sheet

Understand

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.