Opus on conformal symmetry of the Nambu–Goto versus Polyakov strings

Abstract

I investigate the Nambu–Goto and Polyakov strings, accounting for higher-derivative terms in the emergent action for the metric tensor which are classically negligible for smooth metrics but revive quantumly. Using the conformal field theory technique by KPZ-DDK, I compute in the one-loop approximation the conformal dimension and the central charge which differs in the two cases, telling the Nambu–Goto and Polyakov strings apart. I confirm the results by explicit quantum field theory computations of the propagator and the energy–momentum tensor at one loop, using the Pauli–Villars regularization.