A toy model for background independent string field theory

TL;DR

This paper develops a background-independent string field theory model using BRST quantized spinning particles, enabling systematic reduction of fields and coupling to background fields like metric and dilaton.

Contribution

It introduces a novel background-independent extension of the $N=2$ spinning particle model, incorporating non-abelian structures and on-shell/off-shell field coupling.

Findings

Constructed a background-independent algebraic framework.

Derived a model describing an on-shell spin-1 field with background couplings.

Extended the model to include non-abelian gauge structures.

Abstract

We study gauge theories of background fields associated to BRST quantized spinning particle models and identify background-independent algebraic structures which allow to systematically reduce the spectrum of fields and subject some of them to dynamical equations of motion. More specifically, we construct a manifestly background-independent extension of the model based on $N=2$ spinning particle. The resulting system describes an on-shell spin-1 field coupled to off-shell background fields including metric and dilaton. Tensoring with a given Lie algebra results in a non-abelian extension of the model.