The geometry of supersymmetric coset models and superconformal algebras

TL;DR

This paper explores the geometric structure of supersymmetric coset models and their associated superconformal algebras, establishing links between supersymmetry, coset space geometry, and algebraic structures.

Contribution

It provides an on-shell formulation of various supersymmetric coset models and clarifies the correspondence between supersymmetry levels and coset space geometry, connecting current algebras to known superconformal algebras.

Findings

Supersymmetric coset models are characterized by their target space geometry.

Current algebras in these models correspond to specific superconformal algebras.

The (2,2) and (4,0) models relate to N=2 Kazama-Suzuki and N=4 Van Proeyen superconformal algebras.

Abstract

An on-shell formulation of (p,q), 2\leq p \leq 4, 0\leq q\leq 4, supersymmetric coset models with target space the group G and gauge group a subgroup H of G is given. It is shown that there is a correspondence between the number of supersymmetries of a coset model and the geometry of the coset space G/H. The algebras of currents of supersymmetric coset models are superconformal algebras. In particular, the algebras of currents of (2,2) and (4,0) supersymmetric coset models are related to the N=2 Kazama-Suzuki and N=4 Van Proeyen superconformal algebras correspondingly.