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2016

Scale Anomalies, States, and Rates in Conformal Field Theory

Gillioz, Marc, Lu, Xiaochuan, Luty, Markus A.

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This paper presents two methods to compute scale anomaly coefficients in conformal field theories (CFTs), such as the c anomaly in four dimensions, in terms of the CFT data.

We first use Euclidean position space to show that the anomaly coefficient of a four-point function can be computed in the form of an operator product expansion (OPE), namely a weighted sum of OPE coefficients squared.
We compute the weights for scale anomalies associated with scalar operators and show that they are not positive.
We then derive a different sum rule of the same form in Minkowski momentum space where the weights are positive.

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