A Note on Consistent Anomalies

TL;DR

This paper derives the consistent anomalies for superstrings with extended supersymmetry using superfield formalism, unifying previous component-based results and clarifying the relation between small and large N=4 superalgebras.

Contribution

It provides a superfield derivation of anomalies for N=2,3,4 superconformal algebras, including the small N=4 case, and identifies the small N=4 algebra as a constrained version of the large N=4 algebra.

Findings

Derived consistent anomalies for superstrings with extended supersymmetry.

Unified previous component-based results using superfield formalism.

Identified the small N=4 algebra as a constrained large N=4 algebra.

Abstract

Within a BRST formulation, we determine the expressions of the consistent anomaly for superstrings with extended worldsheet supersymmetries of rank N. We consider the O(N) superconformal algebras up to N=4, as well as the `small N=4' superalgebra. This is done using a superfield formalism, allowing to recover previous results that were expressed in components. Moreover, we identify the `small N=4' algebra as the constrained `large N=4' via a self-duality like condition in superspace.