Conformal a-charge, correlation functions and conical defects

TL;DR

This paper shows that the a-charge in conformal anomalies appears in n-point correlation functions of the energy-momentum tensor in flat CFTs with conical defects, providing explicit formulas for various dimensions.

Contribution

It establishes a direct link between the a-charge and correlation functions in CFTs with conical defects, extending previous conjectures with detailed formulas for multiple dimensions.

Findings

a-charge manifests in n-point functions with conical defects

Explicit formulas provided for dimensions 2, 4, 6

General formula derived for arbitrary n

Abstract

In this note we demonstrate that, as we conjectured earlier in [1], the a-charge in the conformal anomaly in dimension $d=2n$ manifests in a $n$-point correlation function of energy momentum tensor of a CFT considered in flat spacetime with a conical defect. We consider in detail dimensions $d=2,\, 4,\, 6$ and give a general formula for arbitrary $n$.