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

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 Lambda, and demonstrate how they result in an anomalous contribution to the string effective action after doing uncertainties Lambda(-2) x Lambda(-2). 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. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

In this study, I investigated the higher-order terms of the Seeley expansion of the heat kernel and their impact on the string effective action, demonstrating anomalous contributions for the Polyakov string consistent with the KPZ-DDK result for the Liouville theory. However, a deviation was found for the Nambu-Goto string formulation, suggesting potential differences between the two string descriptions.