Gauge algebra and diffeomorphisms in string field theory

TL;DR

This paper investigates the gauge algebra of closed string field theory, revealing universal structures in superstrings and off-shell dependencies in bosonic strings, analyzed through $L_ olinebreak_$ algebras.

Contribution

It demonstrates the universality of the superstring gauge algebra at leading order and explores off-shell dependencies and gauge redefinitions in string field theory.

Findings

Superstring gauge algebra is universal at leading order.

Bosonic string algebra depends on vertex choices and symmetrization.

Off-shell information is affected by field-dependent gauge parameter redefinitions.

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.