Building string field theory around non-conformal backgrounds

TL;DR

This paper proposes a novel gauge-invariant string field theory formulation that operates around non-conformal backgrounds, relaxing the traditional requirement of conformal invariance and broadening the scope of string theory applications.

Contribution

It introduces a construction for string field theory on non-conformal backgrounds without relying on conformal invariance, using a generalized BRST operator and a complex of moduli spaces.

Findings

Provides a classical field equation that relaxes conformal invariance constraints.

Develops a geometric framework based on moduli spaces of Riemann surfaces.

Establishes a Batalin-Vilkovisky algebra structure in the complex.

Abstract

The main limitations of string field theory arise because its present formulation requires a background representing a classical solution, a background defined by a strictly conformally invariant theory. Here we sketch a construction for a gauge-invariant string field action around non-conformal backgrounds. The construction makes no reference to any conformal theory. Its two-dimensional field-theoretic aspect is based on a generalized BRST operator satisfying a set of Weyl descent equations. Its geometric aspect uses a complex of moduli spaces of two-dimensional Riemannian manifolds having ordinary punctures, and organized by the number of special punctures which goes from zero to infinity. In this complex there is a Batalin-Vilkovisky algebra that includes naturally the operator which adds one special puncture. We obtain a classical field equation that appears to relax the condition of conformal invariance usually taken to define classical string backgrounds.