Deformations in Closed String Theory -- Canonical Formulation and Regularization

TL;DR

This paper develops a canonical formalism for analyzing deformations in closed string theory, introducing a regularization method that preserves conformal invariance and exploring the geometric properties of the resulting connection.

Contribution

It presents a novel canonical surface integral approach for computing operator commutators in non-holomorphic theories and identifies a unique conformally invariant regularization.

Findings

Regularization respects conformal invariance

Connection is metric compatible and flat

Explicit formulas for operator deformations

Abstract

We study deformations of closed string theory by primary fields of conformal weight $(1,1)$, using conformal techniques on the complex plane. A canonical surface integral formalism for computing commutators in a non-holomorphic theory is constructed, and explicit formul\ae for deformations of operators are given. We identify the unique regularization of the arising divergences that respects conformal invariance, and consider the corresponding parallel transport. The associated connection is metric compatible and carries no curvature.