The Relation between Linear and Non-Linear $N=3,4$ Supergravity Theories

TL;DR

This paper explores the connection between linear and non-linear supergravity theories in two dimensions, showing they are related through a quantum reduction process that equates their quantum currents.

Contribution

It demonstrates that effective actions for $N=3,4$ supergravities with different gauge algebras are related via quantum reduction, establishing identical renormalization factors.

Findings

Effective actions for linear and non-linear supergravities are connected.

Quantum reduction sets quantum currents to zero, linking the theories.

Renormalization factors for both theories are identical.

Abstract

The effective actions for $d=2$, $N=3,4$ chiral supergravities with a linear and a non-linear gauge algebra are related to each other by a quantum reduction, the latter is obtained from the former by putting quantum currents equal to zero. This implies that the renormalisation factors for the quantum actions are identical.