String Tension and the Generation of the Conformal Anomaly

TL;DR

This paper investigates the origin of the string conformal anomaly by analyzing a reformulated string Lagrangian where string tension acts as a small perturbation, revealing tension's role in anomaly generation.

Contribution

It introduces a perturbative approach considering string tension as a small parameter and clarifies how tension influences the conformal anomaly at the quantum level.

Findings

Quantum null strings preserve conformal invariance.

String tension generates the conformal anomaly.

Normal ordering leads to a central charge proportional to tension squared.

Abstract

The origin of the string conformal anomaly is studied in detail. We use a reformulated string Lagrangian which allows to consider the string tension $T_{0}$ as a small perturbation. The expansion parameter is the worldsheet speed of light c, which is proportional to $T_{0}$ . We examine carefully the interplay between a null (tensionless) string and a tensionful string which includes orders $ c^{2} $ and higher. The conformal algebra generated by the constraints is considered. At the quantum level the normal ordering provides a central charge proportional to $ c^{2} $. Thus it is clear that quantum null strings respect conformal invariance and it is the string tension which generates the conformal anomaly.