The Lorentz Anomaly via Operator Product Expansion

TL;DR

This paper provides a detailed derivation of how the critical dimension in string theory arises from the closure of the Lorentz algebra using operator product expansion on the world-sheet.

Contribution

It offers a new detailed derivation of the Lorentz anomaly in string theory based on operator product expansion methods.

Findings

Critical dimension emerges from Lorentz algebra closure

Operator product expansion is key to understanding the anomaly

Classical derivation clarifies the origin of the critical dimension

Abstract

The emergence of a critical dimension is one of the most striking features of string theory. One way to obtain it is by demanding closure of the Lorentz algebra in the light-cone gauge quantisation, as discovered for bosonic strings more than fourty years ago. We give a detailed derivation of this classical result based on the operator product expansion on the Lorentzian world-sheet.