The holomorphic bosonic string

TL;DR

This paper develops a holomorphic version of the bosonic string within a quantum field theory framework, achieving a one-loop exact quantization and connecting algebraic structures to string moduli spaces.

Contribution

It introduces a holomorphic bosonic string model, constructs its quantization, and links algebraic and geometric structures to string theory moduli spaces.

Findings

Critical dimension as an obstruction to quantum master equation

Factorization algebra recovers BRST cohomology

Factorization homology encodes the determinant line bundle

Abstract

We present a holomorphic version of the bosonic string in the formalism of quantum field theory developed by Costello and collaborators. In this paper we focus on the case in which space-time is flat and construct a one-loop exact quantization. Starting from first principles, we arrive at the critical dimension as an obstruction to satisfying the quantum master equation. Moreover, we show how the factorization algebra recovers the BRST cohomology of the string and give another construction of the Gerstenhaber structure. Finally, we show how the factorization homology along closed manifolds encodes the determinant line bundle over the moduli space of Riemann surfaces.