Induced (N,0) supergravity as a constrained Osp(N,2) WZWN model and its effective action

TL;DR

This paper constructs a two-dimensional supergravity theory with various N, derived from a constrained Osp(N|2) WZWN model, and computes its finite one-loop effective action including quantum corrections.

Contribution

It introduces a method to obtain (N,0) supergravity in 2D from constrained Osp(N|2) models and calculates the finite one-loop effective action with quantum corrections.

Findings

Effective action is finite at one loop.

Gauge algebra closes with quantum corrections.

The induced action can be rescaled to include quantum effects.

Abstract

A chiral $(N,0) $ supergravity theory in d=2 dimensions for any $N$ and its induced action can be obtained by constraining the currents of an Osp(N$|$2) WZWN model. The underlying symmetry algebras are the nonlinear SO(N) superconformal algebras of Knizhnik and Bershadsky. The case $N=3$ is worked out in detail. We show that by adding quantum corrections to the classical transformation rules, the gauge algebra on gauge fields and currents closes. Integrability conditions on Ward identities are derived. The effective action is computed at one loop. It is finite, and can be obtained from the induced action by rescaling the central charge and fields by finite Z factors.