A complex geometric perspective on a,c anomalies

TL;DR

This paper explores the relationship between a,c anomalies and supersymmetry in four-dimensional conformal field theories, using a complex geometric approach to connect these coefficients with holomorphic reparametrization symmetry.

Contribution

It establishes a novel link between a,c anomaly coefficients and holomorphic reparametrization symmetry in supersymmetric conformal field theories.

Findings

Proves a relationship between a,c coefficients and anomalies via holomorphic twist.

Connects supersymmetry, anomalies, and complex geometry in 4D CFTs.

Provides a geometric framework for understanding anomaly coefficients.

Abstract

In four-dimensional conformal field theory, the numbers a and c are defined as coefficients of particular terms in the operator product expansion (OPE) of the energy-momentum tensor. With supersymmetry there are relations between these coefficients and mixed R-symmetry and gravitational anomalies. In this paper we prove a relationship between these coefficients and anomalies to holomorphic reparametrization symmetry at the level of the holomorphic twist.