Gauge algebra and diffeomorphisms in string field theory

Abstract

We consider the gauge algebra of closed string field theory with a focus on diffeomorphisms. This algebra contains off-shell information in two ways. The first way is geometric, through the choice of three-punctured sphere defining the three-string vertex. We establish that to leading order in derivatives the superstring algebra is universal: identical for any choice of vertex. For bosonic strings, however, some off-shell dependence remains for vertices that require symmetrization. Off-shell information also appears because field-dependent redefinition of the gauge parameters can alter the algebra. We analyze this dependence in the language of $L_{\infty }$ algebras, looking at the role of trivial gauge transformations in the efforts to demonstrate that standard diffeomorphisms are part of the string gauge symmetry.

31 pages, added references. Added a section 4.1 on the identification of diffeomorphisms in string theory