N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: Symplectic covariance gaugings and the momentum map

Abstract

The general form of N = 2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets, with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in that we use a coordinate independent and manifestly symplectic covariant formalism which allows to cover theories difficult to formulate within superspace or tensor calculus approach. We provide the complete lagrangian and supersymmetry variations with all fermionic terms, and the form of the scalar potential for arbitrary quaternionic manifolds and special geometry, not necessarily in special coordinates. Lagrangians for rigid theories are also written in this general setting and the connection with local theories elucidated. The derivation of these results using geometrical techniques is briefly summarized.

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

“…This requires the choice of a basis in which the θ term (given by Re N ΛΣ in special geometry [34]) is proportional to the axion contained in the vector multiplet. Indeed, in our basis the kinetic vector matrix is N = iz , which has the required property.…”

“…The above term can be further simplified by noting that, when gauging axion symmetries (this actually implies, in the parametrization chosen, that all components of the SU(2) connections are b-independent), we have [34,3,37]…”

On the non-BPS first order flow in $ \mathcal{N} $ = 2 U(1)-gauged Supergravity

“…The only difference with respect to the Lagrangian of the ungauged theory is the scalar potential V g [22]. This is generated by the FI terms G and can be written in a symplectic covariant form as…”

“…The SUSY variations for the gravitino and gaugino, in N = 2 U(1)-gauged SUGRA are [22] 12) where the covariant derivative is 13) with A µ being the Kähler transformations connection…”

Type IIA orientifold compactification on SU(2)-structure manifolds

“…In a consistent N = 2 supergravity Lagrangian, they should couple as [35] 37) where the matrix N is expressed in terms of the prepotential F…”