Curvature formula for the space of 2-d conformal field theories

TL;DR

This paper derives formulas for the curvature tensors of the Riemannian metrics on the spaces of two-dimensional conformal field theories and boundary conformal field theories, providing geometric insights into these theories.

Contribution

It introduces explicit curvature formulas for the moduli spaces of 2D conformal and boundary conformal field theories, advancing the geometric understanding of these spaces.

Findings

Derived the curvature tensor formula for 2D conformal field theories

Derived the curvature tensor formula for boundary conformal field theories

Provided geometric insights into the structure of conformal field theory spaces

Abstract

We derive a formula for the curvature tensor of the natural Riemannian metric on the space of two-dimensional conformal field theories and also a formula for the curvature tensor of the space of boundary conformal field theories.