Canonical Approach to String Theory in Massive Background Fields

TL;DR

This paper develops a canonical gauge invariant quantum formulation for closed bosonic strings interacting with massive background fields, deriving equations of motion that align with string spectrum structure.

Contribution

It introduces a new method for constructing gauge invariant quantum formulations for string theories with massive backgrounds, including a regularization technique and algebra closure analysis.

Findings

Quantum gauge algebra calculated up to linear order in background fields.

Closure of the algebra yields consistent equations of motion for background fields.

Results align with the expected structure of string spectrum.

Abstract

A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive background fields. Choosing an ordering prescription and developing a suitable regularization technique we calculate quantum guage algebra up to linear order in background fields. Requirement of closure for the algebra leads to equations of motion for massive background fields which appear to be consistent with the structure of string spectrum.