Towards the classification of conformal field theories in arbitrary even dimension

TL;DR

This paper classifies a subset of even-dimensional conformal field theories similar to 2D theories, predicting relations between anomaly coefficients and stress-tensor correlators, and verifies these in multiple dimensions.

Contribution

It identifies a class of even-dimensional CFTs where the irreversibility of RG flow applies, extending 2D results to higher even dimensions and providing new predictions.

Findings

Prediction of the ratio between Euler density coefficient and stress-tensor two-point function.

Verification of the prediction in four, six, and eight dimensions.

Extension of the irreversibility formula to massive flows in even dimensions.

Abstract

I identify the class of even-dimensional conformal field theories that is most similar to two-dimensional conformal field theory. In this class the formula, elaborated recently, for the irreversibility of the renormalization-group flow applies also to massive flows. This implies a prediction for the ratio between the coefficient of the Euler density in the trace anomaly (charge a) and the stress-tensor two-point function (charge c). More precisely, the trace anomaly in external gravity is quadratic in the Ricci tensor and the Ricci scalar and contains a unique central charge. I check the prediction in detail in four, six and eight dimensions, and then in arbitrary even dimension.