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

TL;DR

This paper compares Nambu-Goto and Polyakov strings by analyzing their conformal properties at the quantum level, revealing differences in conformal dimensions and central charges through one-loop calculations.

Contribution

It introduces higher-derivative terms in the string actions and computes their quantum conformal data, distinguishing Nambu-Goto from Polyakov strings.

Findings

Conformal dimensions differ between the two string models.

Central charges are computed and found to be distinct.

Results are confirmed via explicit quantum field theory calculations.

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.