Exact solution of higher-derivative conformal theory and minimal models

Summary: I investigate the Nambu-Goto and Polyakov strings, taking into account higher-derivative terms in the emergent action for the metric tensor. These terms are classically negligible but become relevant quantumly. Using the conformal field theory technique by KPZ-DDK, I compute the conformal dimension and central charge in the one-loop approximation, which distinguish the Nambu-Goto and Polyakov strings. I confirm the results by explicit quantum field theory computations and Pauli-Villars regularization.

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.