Duality Transformations in Supersymmetric Yang-Mills Theories coupled to Supergravity,

TL;DR

This paper develops a symplectic covariant framework to analyze duality symmetries in N=2 supergravity coupled to Yang--Mills theories, including stringy dualities and implications for extended supergravities.

Contribution

It introduces a general, coordinate covariant approach to duality transformations in N=2 supergravity theories, applicable even without a holomorphic prepotential, and explores their physical implications.

Findings

Established a symplectic covariant framework for dualities.

Derived expressions for physical quantities without a prepotential.

Analyzed duality effects on BPS spectrum and supergravity theories.

Abstract

We consider duality transformations in N=2, d=4 Yang--Mills theory coupled to N=2 supergravity. A symplectic and coordinate covariant framework is established, which allows one to discuss stringy `classical and quantum duality symmetries' (monodromies), incorporating T and S dualities. In particular, we shall be able to study theories (like N=2 heterotic strings) which are formulated in symplectic basis where a `holomorphic prepotential' F does not exist, and yet give general expressions for all relevant physical quantities. Duality transformations and symmetries for the N=1 matter coupled Yang--Mills supergravity system are also exhibited. The implications of duality symmetry on all N>2 extended supergravities are briefly mentioned. We finally give the general form of the central charge and the N=2 semiclassical spectrum of the dyonic BPS saturated states (as it comes by truncation of the N=4 spectrum).