On Homotopy Algebras and Quantum String Field Theory

TL;DR

This paper explores the mathematical structure of string field theories using homotopy algebra, establishing connections between open and closed strings, and analyzing quantum obstructions and background independence.

Contribution

It applies homotopy algebra techniques to analyze the existence, uniqueness, and background independence of various string field theories at classical and quantum levels.

Findings

Open string theories correspond to closed string backgrounds.

Quantum obstructions can prevent background independence.

Loop homotopy algebras ensure uniqueness of closed string theories.

Abstract

We revisit the existence, background independence and uniqueness of closed, open and open-closed bosonic- and topological string field theory, using the machinery of homotopy algebra. In a theory of classical open- and closed strings, the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. We then discuss obstructions of these moduli spaces at the quantum level. For the quantum theory of closed strings, uniqueness on a given background follows from the decomposition theorem for loop homotopy algebras. We also address the question of background independence of closed string field theory.