Spinorial cohomology and maximally supersymmetric theories

Fields in supersymmetric gauge theories may be seen as elements in a spinorial cohomology. We elaborate on this subject, specialising to maximally supersymmetric theories, where the superspace Bianchi identities, after suitable conventional constraints are imposed, put the theories on shell. In these cases, the spinorial cohomologies describe in a unified manner gauge transformations, fields and possible deformations of the models, e.g. string-related corrections in an alpha' expansion. Explicit cohomologies are calculated for super-Yang-Mills theory in D=10, for the N=(2,0) tensor multiplet in D=6 and for supergravity in D=11, in the latter case from the point of view of both the super-vielbein and the super-3-form potential. The techniques may shed light on some questions concerning the alpha'-corrected effective theories, and result in better understanding of the role of the 3-form in D=11 supergravity.Comment: 23 pp, plain tex. v2: Minor changes, references adde

Three-dimensional N=8 conformal supergravity and its coupling to BLG M2-branes

This paper is concerned with the problem of coupling the N=8 superconformal Bagger-Lambert-Gustavsson (BLG) theory to N=8 conformal supergravity in three dimensions. We start by constructing the on-shell N=8 conformal supergravity in three dimensions consisting of a Chern-Simons type term for each of the gauge fields: the spin connection, the SO(8) R-symmetry gauge field and the spin 3/2 Rarita-Schwinger (gravitino) field. We then proceed to couple this theory to the BLG theory. The final theory should have the same physical content, i.e., degrees of freedom, as the ordinary BLG theory. We discuss briefly the properties of this "topologically gauged" BLG theory and why this theory may be useful.Comment: 20 pages, v2: references and comments added, presentation in section 3.2 extended. v3: misprints and a sign error corrected, version published in JHE

On the Dirac-Born-Infeld Action for D-branes

In this note, we consider the reformulation of the Dirac-Born-Infeld action for a Dirichlet p-brane in Brink-Di Vecchia-Howe-Tucker form, i.e., including an independent non-propagating world-volume metric. When p>2, the action becomes non-polynomial. A closed expression is derived for p=3. For selfdual field-strengths, the DBI action is reproduced by an action with a simple F^2 term. We speculate on supersymmetrization of the D_3-brane action. We also give the governing equations for arbitrary p, and derive an implicit expression for the D_4-brane lagrangian.Comment: Plain TeX, 7 pages, TeX file and one postscript figure in compressed tar archiv

Entropy function for rotating extremal black holes in very special geometry

We use the relation between extremal black hole solutions in five- and in four-dimensional N=2 supergravity theories with cubic prepotentials to define the entropy function for extremal black holes with one angular momentum in five dimensions. We construct two types of solutions to the associated attractor equations.Comment: 15 pages, minor change

Spinorial cohomology of abelian d=10 super-Yang-Mills at alpha'^3

We compute the spinorial cohomology of ten-dimensional abelian SYM at order alpha'^3 and we find that it is trivial. Consequently, linear supersymmetry alone excludes the presence of alpha'^3-order corrections. Our result lends support to the conjecture that there may be a unique supersymmetric deformation of ordinary ten-dimensional abelian SYM.Comment: 13 pages, 1 figure, harvma

New supersymmetric AdS4 type II vacua

Building on our recent results on dynamic SU(3)xSU(3) structures we present a set of sufficient conditions for supersymmetric AdS4xM6 backgrounds of type IIA/IIB supergravity. These conditions ensure that the background solves, besides the supersymmetry equations, all the equations of motion of type II supergravity. The conditions state that the internal manifold is locally a codimension-one foliation such that the five dimensional leaves admit a Sasaki-Einstein structure. In type IIA the supersymmetry is N=2, and the total six-dimensional internal space is locally an S^2 bundle over a four-dimensional Kaehler-Einstein base; in IIB the internal space is the direct product of a circle and a five-dimensional squashed Sasaki-Einstein manifold. Given any five-dimensional Sasaki-Einstein manifold we construct the corresponding families of type IIA/IIB vacua. The precise profiles of all the fields are determined at the solution and depend on whether one is in IIA or in IIB. In particular the background does not contain any sources, all fluxes (including the Romans mass in IIA) are generally non-zero, and the dilaton and warp factor are non-constant.Comment: 19 pages; clarifications added, version to appear in JHE

Black Holes in Supergravity: the non-BPS Branch

We construct extremal, spherically symmetric black hole solutions to 4D supergravity with charge assignments that preclude BPS-saturation. In particular, we determine the ground state energy as a function of charges and moduli. We find that the mass of the non-BPS black hole remains that of a marginal bound state of four basic constituents throughout the entire moduli space and that there is always a non-zero gap above the BPS bound.Comment: 29 pages, one appendix, no figures; v2. few comments and references added and a missing sign included; v3. further references adde

A second look at N=1 supersymmetric AdS_4 vacua of type IIA supergravity

We show that a class of type IIA vacua recently found within the N=4 effective approach corresponds to compactification on Ads_4 \times S^3 \times S^3/Z_2^3. The results obtained using the effective method completely match the general ten-dimensional analysis for the existence of N=1 warped compactifications on Ads_4 \times M_6. In particular, we verify that the internal metric is nearly-Kahler and that for specific values of the parameters the Bianchi identity of the RR 2-form is fulfilled without sources. For another range of parameters, including the massless case, the Bianchi identity is satisfied when D6-branes are introduced. Solving the tadpole cancellation conditions in D=4 we are able to find examples of appropriate sets of branes. In the second part of this paper we describe how an example with internal space CP^3 but with non nearly-Kahler metric fits into the general analysis of flux vacua.Comment: Latex file, 35 pages, no figures. Reference added, minor corrections adde

D-Brane Potentials from Multi-Trace Deformations in AdS/CFT

It is known that certain AdS boundary conditions allow smooth initial data to evolve into a big crunch. To study this type of cosmological singularity, one can use the dual quantum field theory, where the non-standard boundary conditions are reflected by the presence of a multi-trace potential unbounded below. For specific AdS_4 and AdS_5 models, we provide a D-brane (or M-brane) interpretation of the unbounded potential. Using probe brane computations, we show that the AdS boundary conditions of interest cause spherical branes to be pushed to the boundary of AdS in finite time, and that the corresponding potential agrees with the multi-trace deformation of the dual field theory. Systems with expanding spherical D3-branes are related to big crunch supergravity solutions by a phenomenon similar to geometric transition.Comment: 26 pages, 3 figures, v4: a few typos fixed

First-order flow equations for extremal black holes in very special geometry

We construct interpolating solutions describing single-center static extremal non-supersymmetric black holes in four-dimensional N=2 supergravity theories with cubic prepotentials. To this end, we derive and solve first-order flow equations for rotating electrically charged extremal black holes in a Taub-NUT geometry in five dimensions. We then use the connection between five- and four-dimensional extremal black holes to obtain four-dimensional flow equations and we give the corresponding solutions.Comment: 21 pages. v2: Summary section adde