Duality transformations in supersymmetric Yang-Mills theories coupled to supergravity

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).

N= 2 Super-Higgs,N= 1 Poincaré Vacua and Quaternionic Geometry

“…A crucial point of this gauging is that it must be formulated in a duality basis [27] for special geometry which has a degenerate holomorphic section X Λ (z) (and where no function F (X) exists) [28,21], that is in a basis non locally related to the "standard" one (1.1). This is because otherwise it would be impossible to break N = 2 → N = 1 since N = 2 would be either unbroken or completely broken [29,30].…”

Electric-magnetic dualities in supergravity

“…However, I should mention that these systems of vector multiplets give rise to special geometry. Again, I refrain from giving further details and refer to the literature (see, e.g., [50][51][52][53]). …”

“…Therefore I must insist that the function F exists. After integrating out the auxiliary tensor it is possible to reformulate the theory in such a way that the function F no longer needs to exist, as long as the periods (X I , F J ) can be written down consistently [51].…”

Self-dual strings and N = 2 supersymmetric field theory

“…[7,8,9]). The BPS states correspond to self-dual 2 strings [10,9,11,12] that wind 1 However within SW theory the stable BPS states can be determined using symmetry arguments [6].…”