Quantum gauging from classical gauging of nonlinear algebras

TL;DR

This paper extends classical nonlinear algebra gauging to the quantum level, showing how anomalies and quantum corrections influence gauge transformations and structure constants, with implications for quantum gauge algebra closure.

Contribution

It introduces a method to incorporate anomalies into quantum gauging of nonlinear algebras, demonstrating the quantum closure of gauge algebras in the large central charge limit.

Findings

Quantum corrections renormalize structure constants.

Quantum gauge algebra closes at large central charge.

Examples illustrate the quantum gauging process.

Abstract

We extend the theory of the gauging of classical quadratically nonlinear algebras without a central charge but with a coset structure, to the quantum level. Inserting the minimal anomalies into the classical transformation rules of the currents introduces further quantum corrections to the classical transformation rules of the gauge fields and currents which additively renormalize the structure constants. The corresponding Ward identities are the c -> infinity limit of the full quantum Ward identities, and reveal that the c -> infinity limit of the quantum gauge algebra closes on fields and currents. Two examples are given.