On higher-order corrections in M theory

A theoretical analysis of higher-order corrections to D=11 supergravity is given in a superspace framework. It is shown that any deformation of D=11 supergravity for which the lowest-dimensional component of the four-form $G_4$ vanishes is trivial. This implies that the equations of motion of D=11 supergravity are specified by an element of a certain spinorial cohomology group and generalises previous results obtained using spinorial or pure spinor cohomology to the fully non-linear theory. The first deformation of the theory is given by an element of a different spinorial cohomology group with coefficients which are local tensorial functions of the massless supergravity fields. The four-form Bianchi Identities are solved, to first order and at dimension $-{1/2}$, in the case that the lowest-dimensional component of $G_4$ is non-zero. Moreover, it is shown how one can calculate the first-order correction to the dimension-zero torsion and thus to the supergravity equations of motion given an explicit expression for this object in terms of the supergravity fields. The version of the theory with both a four-form and a seven-form is discussed in the presence of the five-brane anomaly-cancelling term. It is shown that the supersymmetric completion of this term exists and it is argued that it is the unique anomaly-cancelling invariant at this dimension which is at least quartic in the fields. This implies that the first deformation of the theory is completely determined by the anomaly term from which one can, in principle, read off the corrections to all of the superspace field strength tensors.Comment: 32 pages. v2: Two references added in the text; footnote adde

D-brane probes on G2 Orbifolds

We consider type IIB string theory on a seven dimensional orbifold with holonomy in G2. The motivation is to use D1-branes as probes of the geometry. The low energy theory on the D1-brane is a sigma-model with two real supercharges (N = (1,1) in two dimensional language). We study in detail the closed and open string sectors and propose a coupling of the twisted fields to the brane that modifies the vacuum moduli space so that the singularity at the origin is removed. Instead of coming from D-terms, which are not present here, the modification comes from a ``twisted'' mass term for the seven scalar multiplets on the brane. The proposed mechanism involves a generalization of the moment map.Comment: 16 pages; v2: References added; v3: Erroneous interpretation of twisted moduli corrected, acknowledgments adde

The deformed M2-brane

The superembedding formalism is used to study correction terms to the dynamics of the M2 brane in a flat background. This is done by deforming the standard embedding constraint. It is shown rigorously that the first such correction occurs at dimension four. Cohomological techniques are used to determine this correction explicitly. The action is derived to quadratic order in fermions, and the modified \k-symmetry transformations are given.Comment: 38 pages, 3 figure

Massive IIA supergravities

We perform a systematic search for all possible massive deformations of IIA supergravity in ten dimensions. We show that there exist exactly two possibilities: Romans supergravity and Howe-Lambert-West supergravity. Along the way we give the full details of the ten-dimensional superspace formulation of the latter. The scalar superfield at canonical mass dimension zero (whose lowest component is the dilaton), present in both Romans and massless IIA supergravities, is not introduced from the outset but its existence follows from a certain integrability condition implied by the Bianchi identities. This fact leads to the possibility for a certain topological modification of massless IIA, reflecting an analogous situation in eleven dimensions.Comment: 35 pages; v2: typos corrected, added eq. (A4

Dirac Action on M5 and M2 Branes with Bulk Fluxes

We derive an explicit form of the quadratic in fermions Dirac action on the M5 brane for an arbitrary on-shell background of 11D supergravity with non-vanishing fluxes and in presence of a chiral 2-form on M5. This action may be used to generalize the conditions for which the non-perturbative superpotential can be generated in M/string theory. We also derive the Dirac action with bulk fluxes on the M2 brane.Comment: 12 pages References adde

Generalized geometry, calibrations and supersymmetry in diverse dimensions

We consider type II backgrounds of the form R^{1,d-1} x M^{10-d} for even d, preserving 2^{d/2} real supercharges; for d = 4, 6, 8 this is minimal supersymmetry in d dimensions, while for d = 2 it is N = (2,0) supersymmetry in two dimensions. For d = 6 we prove, by explicitly solving the Killing-spinor equations, that there is a one-to-one correspondence between background supersymmetry equations in pure-spinor form and D-brane generalized calibrations; this correspondence had been known to hold in the d = 4 case. Assuming the correspondence to hold for all d, we list the calibration forms for all admissible D-branes, as well as the background supersymmetry equations in pure-spinor form. We find a number of general features, including the following: The pattern of codimensions at which each calibration form appears exhibits a (mod 4) periodicity. In all cases one of the pure-spinor equations implies that the internal manifold is generalized Calabi-Yau. Our results are manifestly invariant under generalized mirror symmetry.Comment: 28 pages, 1 tabl

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

The holonomy of IIB supercovariant connection

We show that the holonomy of the supercovariant connection of IIB supergravity is contained in SL(32, \bR). We also find that the holonomy reduces to a subgroup of SL(32-N)\st (\oplus^N \bR^{32-N}) for IIB supergravity backgrounds with $N$ Killing spinors. We give the necessary and sufficient conditions for a IIB background to admit $N$ Killing spinors. A IIB supersymmetric probe configuration can involve up to 31 linearly independent planar branes and preserves one supersymmetry.Comment: 8 pages, latex. v2: Minor correction