Luca Sommovigo

D = 4, N=2 gauged supergravity in the presence of tensor multiplets

Abstract Using superspace techniques we construct the general theory describing D=4, N =2 supergravity coupled to an arbitrary number of vector and scalar-tensor multiplets. The scalar manifold of the theory is the direct product of a special Kahler and a reduction of a quaternionic-Kahler manifold. We perform the electric gauging of a subgroup of the isometries of such manifold as well as “magnetic” deformations of the theory discussing the consistency conditions arising in this process. The resulting scalar potential is the sum of a symplectic invariant part (which in some instances can be recast into the standard form of the gauged N =2 theory) and of a non-invariant part both giving new deformations. We also show the relation of such theories to flux compactifications of type II string theories.

N = 2 supergravity lagrangian coupled to tensor multiplets with electric and magnetic fluxes

We derive the full N = 2 supergravity lagrangian which contains a symplectic invariant scalar potential in terms of electric and magnetic charges. As shown in reference [1], the appearance of magnetic charges is allowed only if tensor multiplets are present and a suitable Fayet-Iliopoulos term is included in the fermion transformation laws. We generalize the procedure in the quoted reference by adding further a Fayet-Iliopoulos term which allows the introduction of electric charges in such a way that the potential and the equations of motion of the theory are symplectic invariant. The theory is further generalized to include an ordinary electric gauging and the form of the resulting scalar potential is given.

On D=4, N=2 supergravity with Abelian electric and magnetic charges

Abstract We discuss the relation between standard N = 2 supergravity with translational gauging and N = 2 supergravities with scalar-tensor multiplets with massive tensors and Abelian electric charges. We point out that a symplectic covariant formulation of N = 2 supergravity can be achieved just in the presence of tensor multiplets. As a consequence one can see that the formulation of the N = 2 theory as it comes from IIB flux compactification, which is included in these models, is equivalent to a non-perturbative phase of standard N = 2 supergravity. It is also shown that the IIB tadpole cancellation condition is imposed by supersymmetry in four dimensions.

Poincaré dual of D=4, N=2 supergravity with tensor multiplets

Abstract We study, in an arbitrary even number D of dimensions, the duality between massive D / 2 tensors coupled to vectors, with masses given by an arbitrary number of “electric” and “magnetic” charges, and ( D / 2 − 1 ) massive tensors. We develop a formalism to dualize the Lagrangian of D = 4 , N = 2 supergravity coupled to tensor and vector multiplets, and show that, after the dualization, it is equivalent to a standard D = 4 , N = 2 gauged supergravity in which the special geometry quantities have been acted on by a suitable symplectic rotation.

Theory of superdualities and the orthosymplectic supergroup

Abstract We study the dualities for sigma models with fermions and bosons. We found that the generalization of the SO ( m , m ) duality for D = 2 sigma models and the Sp ( 2 n ) duality for D = 4 sigma models is the orthosymplectic duality OSp ( m , m | 2 n ) . We study the implications of this and we derive the most general D = 2 sigma model, coupled to fermionic and bosonic one-forms, with such dualities. To achieve this we generalize Gaillard–Zumino analysis to orthosymplectic dualities, which requires to define embedding of the superisometry group of the target space into the duality group. We finally discuss the recently proposed fermionic dualities as a by-product of our construction.

D=4, N=2 Gauged Supergravity coupled to Vector-Tensor Multiplets

Abstract We construct the general four–dimensional N = 2 supergravity theory coupled to vector and vector–tensor multiplets only. Consistency of the construction requires the introduction of the vector fields dual to those sitting in the same supermultiplets as the antisymmetric tensors, as well as the scalar fields dual to the tensors themselves. Gauge symmetries also involving these additional fields guarantee the correct counting of the physical degrees of freedom.

Penrose limit of AdS3 × S3 × S3 × S1 and its associated σ-model

We study the Penrose limit of a supersymmetric IIB background, with non-trivial NS 3-form field strength, obtaining a solution with the smallest number of supercharges (i.e. 16) allowed; we write down explicitly the superalgebra of the theory, build the supersymmetric associated IIB string sigma model and make conjectures on the dual gauge theory.

Supersymmetric Fluid Dynamics

Recently Navier-Stokes (NS) equations have been derived from the duality between the black branes and a conformal fluid on the boundary of AdS5. Nevertheless, the full correspondence has to be established between solutions of supergravity in AdS5 and supersymmetric field theories on the boundary. That prompts the construction of NS equations for a supersymmetric fluid. In the framework of rigid susy, there are several possibilities and we propose one candidate. We deduce the equations of motion in two ways: both from the divergenless condition on the energy-momentum tensor and by a suitable parametrization of the auxiliary fields. We give the complete component expansion and a very preliminary analysis of the physics of this supersymmetric fluid.

TRIALITY INVARIANCE IN THE N=2 SUPERSTRING

Abstract We prove the discrete triality invariance of the N = 2 NSR superstring moving in a D = 2 + 2 target space. We find that triality holds also in the Siegel–Berkovits formulation of the selfdual superstring. A supersymmetric generalization of Cayleys hyperdeterminant, based on a quartic invariant of the SL ( 2 | 1 ) 3 superalgebra, is presented.

Penrose limit of AdS(3) X S(3) X S(3) X S(1) and its associated sigma model

We study the Penrose limit of a supersymmetric IIB background, with non-trivial NS 3-form field strength, obtaining a solution with the smallest number of supercharges (i.e. 16) allowed; we write down explicitly the superalgebra of the theory, build the supersymmetric associated IIB string sigma model and make conjectures on the dual gauge theory.