Background Independent Algebraic Structures in Closed String Field Theory

TL;DR

This paper constructs a background-independent Batalin-Vilkovisky algebra on moduli spaces of Riemann surfaces, providing a new algebraic framework for closed string field theory that does not rely on a conformal field theory state space.

Contribution

It introduces a novel background-independent BV algebra structure on moduli spaces, linking it to closed string gauge algebra without referencing a specific conformal field theory.

Findings

Established a BV algebra on moduli spaces of Riemann surfaces.

Defined a cohomology class of the operator δ for string vertices.

Constructed a background-independent Lie algebra for closed string gauge symmetry.

Abstract

We construct a Batalin-Vilkovisky (BV) algebra on moduli spaces of Riemann surfaces. This algebra is background independent in that it makes no reference to a state space of a conformal field theory. Conformal theories define a homomorphism of this algebra to the BV algebra of string functionals. The construction begins with a graded-commutative free associative algebra $\C$ built from the vector space whose elements are orientable subspaces of moduli spaces of punctured Riemann surfaces. The typical element here is a surface with several connected components. The operation $\Delta$ of sewing two punctures with a full twist is shown to be an odd, second order derivation that squares to zero. It follows that $(\C, \Delta)$ is a Batalin-Vilkovisky algebra. We introduce the odd operator $\delta = \partial + \hbar\Delta$, where $\partial$ is the boundary operator. It is seen that $\delta^2=0$, and that consistent closed string vertices define a cohomology class of $\delta$. This cohomology class is used to construct a Lie algebra on a quotient space of $\C$. This Lie algebra gives a manifestly background independent description of a subalgebra of the closed string gauge algebra.