Towards the classification of conformal field theories in arbitrary even dimension

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.

9 pages

References in corpus (1)

• Anomalies, Unitarity and Quantum Irreversibility

Cited by in corpus (13)

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• Simple recipe for holographic Weyl anomaly
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• On the Canonical c-Function in 4-d Field Theories Possessing Supergravity Duals
• A universal flow invariant in quantum field theory
• A different kind of four dimensional brane for string theory
• A note on the improvement ambiguity of the stress tensor and the critical limits of correlation functions