We set up the formalism of holographic renormalization for the matter-coupled two-dimensional maximal supergravity that captures the low-lying fluctuations around the non-conformal D0-brane near-horizon geometry. As an application we compute holograp
hically one- and two-point functions of the BFSS matrix quantum mechanics and its supersymmetric $SO(3)times SO(6)$ deformation.
We determine the most general form of off-shell N=(1,1) supergravity field configurations in three dimensions by requiring that at least one off-shell Killing spinor exists. We then impose the field equations of the topologically massive off-shell su
pergravity and find a class of solutions whose properties crucially depend on the norm of the auxiliary vector field. These are spacelike-squashed and timelike-stretched AdS_3 for the spacelike and timelike norms, respectively. At the transition point where the norm vanishes, the solution is null warped AdS_3. This occurs when the coefficient of the Lorentz-Chern-Simons term is related to the AdS radius by $muell=2$. We find that the spacelike-squashed AdS_3 can be modded out by a suitable discrete subgroup of the isometry group, yielding an extremal black hole solution which avoid closed timelike curves.
We construct six-dimensional superconformal models with non-abelian tensor and hypermultiplets. They describe the field content of (2,0) theories, coupled to (1,0) vector multiplets. The latter are part of the non-abelian gauge structure that also in
cludes non-dynamical three- and four-forms. The hypermultiplets are described by gauged nonlinear sigma models with a hyper-Kaehler cone target space. We also address the question of constraints in these models and show that their resolution requires the inclusion of abelian factors. These provide couplings that were previously considered for anomaly cancellations with abelian tensor multiplets and resulted in the selection of ADE gauge groups.
We construct rigid supersymmetric theories for interacting vector and tensor multiplets on six-dimensional Riemannian spin manifolds. Analyzing the Killing spinor equations, we derive the constraints on these theories. To this end, we reformulate the
conditions for supersymmetry as a set of necessary and sufficient conditions on the geometry. The formalism is illustrated with a number of examples, including manifolds that are hermitian, strong Kaehler with torsion. As an application, we show that the path integral of pure super Yang-Mills theory defined on a Calabi-Yau threefold M_6 localizes on stable holomorphic bundles over M_6.
The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective field streng
ths are dual to each other. It is well known that such equations can be integrated to a local action that carries on equal footing the p-forms together with their duals and is manifestly duality invariant. Space-time covariance is no longer manifest but still present with a non-standard realization of space-time diffeomorphisms on the gauge fields. In this paper, we give a non-abelian generalization of this first-order action by gauging part of its global symmetries. The resulting field equations are non-abeli
We construct maximal supergravity in four dimensions with local scaling symmetry as deformation of the original Cremmer-Julia theory. The different theories which include the standard gaugings are parametrized by an embedding tensor carrying 56+912 p
arameters. We determine the form of the possible gauge groups and work out the complete set of field equations. As a result we obtain the most general couplings compatible with N=8 supersymmetry in four dimensions. A particular feature of these theories is the absence of an action and an additional positive contribution to the effective cosmological constant. Moreover, these gaugings are generically dyonic, i.e. involve simultaneously electric and magnetic vector fields.
