We construct the Hodge dual for supermanifolds by means of the Grassmannian Fourier transform of superforms. In the case of supermanifolds it is known that the superforms are not sufficient to construct a consistent integration theory and that the in
tegral forms are needed. They are distribution-like forms which can be integrated on supermanifolds as a top form can be integrated on a conventional manifold. In our construction of the Hodge dual of superforms they arise naturally. The compatibility between Hodge duality and supersymmetry is exploited and applied to several examples. We define the irreducible representations of supersymmetry in terms of integral and superforms in a new way which can be easily generalised to several models in different dimensions. The construction of supersymmetric actions based on the Hodge duality is presented and new supersymmetric actions with higher derivative terms are found. These terms are required by the invertibility of the Hodge operator.
Integral forms provide a natural and powerful tool for the construction of supergravity actions. They are generalizations of usual differential forms and are needed for a consistent theory of integration on supermanifolds. The group geometrical appro
ach to supergravity and its variational principle are reformulated and clarified in this language. Central in our analysis is the Poincare dual of a bosonic manifold embedded into a supermanifold. Finally, using integral forms we provide a proof of Gates so-called Ectoplasmic Integration Theorem, relating superfield actions to component actions.
Recently, a Lagrangian description of superfluids attracted some interest from the fluid/gravity-correspondence viewpoint. In this respect, the work of Dubovksy et al. has proposed a new field theoretical description of fluids, which has several inte
resting aspects. On another side, we have provided in arXiv:1304.2206 a supersymmetric extension of the original works. In the analysis of the Lagrangian structures a new invariant appeared which, although related to known invariants, provides, in our opinion, a better parametrisation of the fluid dynamics in order to describe the fluid/superfluid phases.
We compute the wig for the BTZ black hole, namely the complete non-linear solution of supergravity equations with all fermionic zero modes. We use a gauge completion method starting from AdS_3 Killing spinors to generate the gravitinos fields associa
ted to the BH and we compute the back-reaction on the metric. Due to the anticommutative properties of the fermionic hairs the resummation of these effects truncates at some order. We illustrate the technique proposed in a precedent paper in a very explicit and analytical form. We also compute the mass, the angular momentum and other charges with their corrections.
We use Pure Spinor string theory to construct suitable kinematical factors which explicitly satisfy the Kleiss-Kuijf (KK) relations. Using the formula conceived by Bern et al. and employed by us for 4- and 5-point amplitudes in a previous work, we ar
e able to compute the 6-point supergravity amplitude from the corresponding SYM building blocks given by Mafra et al.. We derive the KK and Bern-Carrasco-Johansson (BCJ) identities from the BRST invariance and we discuss the relations between Bern et al. building blocks and those of Mafra et al..
Recently Navier-Stokes (NS) equations have been derived from the duality between the black branes and a conformal fluid on the boundary of AdS_5. Nevertheless, the full correspondence has to be established between solutions of supergravity in AdS_5 a
nd 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.
Recently the Navier-Stokes equations have been derived from the duality with the black branes in AdS_5. The zero modes of black branes are reinterpreted as dynamical degrees of freedom of a conformal fluid on the boundary of AdS_5. Here, we derive th
e corrections to the Navier-Stokes equations due to fermionic zero modes of the black branes. We study only the contributions due to bilinears in the fermionic zero modes in the first order of the parameter expansion. The need of a superextension of the fluid dynamics is a consequence of the full AdS/CFT correspondence and yet to be investigated.
We study two aspects of fermionic T-duality: the duality in purely fermionic sigma models exploring the possible obstructions and the extension of the T-duality beyond classical approximation. We consider fermionic sigma models as coset models of sup
ergroups divided by their maximally bosonic subgroup OSp(m|n)/SO(m) x Sp(n). Using the non-abelian T-duality and a non-conventional gauge fixing we derive their fermionic T-duals. In the second part of the paper, we prove the conformal invariance of these models at one and two loops using the Background Field Method and we check the Ward Identities.
We present a study on the integral forms and their Cech/de Rham cohomology. We analyze the problem from a general perspective of sheaf theory and we explore examples in superprojective manifolds. Integral forms are fundamental in the theory of integr
ation in supermanifolds. One can define the integral forms introducing a new sheaf containing, among other objects, the new basic forms delta(dtheta) where the symbol delta has the usual formal properties of Diracs delta distribution and acts on functions and forms as a Dirac measure. They satisfy in addition some new relations on the sheaf. It turns out that the enlarged sheaf of integral and ordinary superforms contains also forms of negative degree and, moreover, due to the additional relations introduced, its cohomology is, in a non trivial way, different from the usual superform cohomology.
We derive the Free Differential Algebra for type IIA supergravity in 10 dimensions in the string frame. We provide all fermionic terms for all curvatures. We derive the Green-Schwarz sigma model for type IIA superstring based on the FDA construction
and we check its invariance under kappa-symmetry. Finally, we derive the pure spinor sigma model and we check the BRST invariance. The present derivation has the advantage that the resulting sigma model is constructed in terms of the superfields appearing in the FDA and therefore one can directly relate a supergravity background with the corresponding sigma model. The complete explicit form of the BRST transformations is given and some new pure spinor constraints are obtained. Finally, the explicit form of the action is given.
