Private life of the Liouville field that causes new anomalies in the Nambu-Goto string

Abstract

I consider higher-order terms of the Seeley expansion of the heat kernel, which for smooth metrics are suppressed as inverse powers of the UV cutoff Λ, and demonstrate how they result in an anomalous contribution to the string effective action after doing uncertainties Λ−2×Λ2. For the Polyakov string these anomalies precisely reproduce at one loop the result of KPZ-DDK obtained for the Liouville theory by the conformal field theory technique. For the Nambu-Goto string I find a deviation from this result which shows that the two string formulations may differ.

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