Quantum version of the N=8 superconformal algebra

TL;DR

This paper investigates the quantum structure of the soft N=8 superconformal algebra, revealing anomalies, quantum corrections, and constructing a nilpotent BRST operator, extending previous work on related algebras.

Contribution

It provides the first detailed analysis of the quantum properties of the N=8 superconformal algebra, including anomaly classification and BRST operator construction.

Findings

Operator product expansions exhibit a one-parameter class of anomalies.

Quantum corrections can shift anomalies, enabling a nilpotent BRST operator.

A Fock-space representation with unusual mode behavior is constructed.

Abstract

The quantized form of the soft N=8 superconformal algebra is investigated. Its operator product expansions are shown to exhibit a one-parameter-class of (soft) anomalies, which may be arbitrarily shifted by certain suitable quantum corrections of the generators. In particular, the BRST operator can be constructed and made nilpotent in the quantum version of all known realizations of the algebra. This generalizes the results of Cederwall and Preitschopf, who studied the $\widehat{S^7}$-algebra, that is contained as a soft Kac-Moody part in the superconformal algebra. A Fock-space representation is given, that has to be somewhat unusual in certain modes.