Finite Deformations of Conformal Field Theories Using Analytically Regularized Connections

TL;DR

This paper introduces an analytical regularization method for studying finite deformations of conformal field theories, demonstrating that the resulting connections are flat and preserve conformal invariance, enabling well-defined finite parallel transport.

Contribution

It develops a new regularization approach for conformal field theory deformations that ensures integrability and flatness of the associated connections, facilitating finite deformations analysis.

Findings

Connections are flat and integrable.

Regularization preserves conformal invariance.

Finite parallel transport is well-defined.

Abstract

We study some natural connections on spaces of conformal field theories using an analytical regularization method. The connections are based on marginal conformal field theory deformations. We show that the analytical regularization preserves conformal invariance and leads to integrability of the marginal deformations. The connections are shown to be flat and to generate well-defined finite parallel transport. These finite parallel transports yield formulations of the deformed theories in the state space of an undeformed theory. The restrictions of the connections to the tangent space are curved but free of torsion.