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

Aspects of higher curvature terms and U-duality

We discuss various aspects of dimensional reduction of gravity with the Einstein-Hilbert action supplemented by a lowest order deformation formed as the Riemann tensor raised to powers two, three or four. In the case of R^2 we give an explicit expression, and discuss the possibility of extended coset symmetries, especially SL(n+1,Z) for reduction on an n-torus to three dimensions. Then we start an investigation of the dimensional reduction of R^3 and R^4 by calculating some terms relevant for the coset formulation, aiming in particular towards E_8(8)/(Spin(16)/Z_2) in three dimensions and an investigation of the derivative structure. We emphasise some issues concerning the need for the introduction of non-scalar automorphic forms in order to realise certain expected enhanced symmetries.Comment: 26 pp., 15 figs., plain te

An M-theory solution generating technique and SL(2,R)

In this paper we generalize the O(p+1,p+1) solution generating technique (this is a method used to deform Dp-branes by turning on a NS-NS B-field) to M-theory, in order to be able to deform M5-brane supergravity solutions directly in eleven dimensions, by turning on a non zero three form A. We find that deforming the M5-brane, in some cases, corresponds to performing certain SL(2,R) transformations of the Kahler structure parameter for the three-torus, on which the M5-brane has been compactified. We show that this new M-theory solution generating technique can be reduced to the O(p+1,p+1) solution generating technique with p=4. Further, we find that it implies that the open membrane metric and generalized noncommutativity parameter are manifestly deformation independent for electric and light-like deformations. We also generalize the O(p+1,p+1) method to the type IIA/B NS5-brane in order to be able to deform NS5-branes with RR three and two forms, respectively. In the type IIA case we use the newly obtained solution generating technique and deformation independence to derive a covariant expression for an open D2-brane coupling, relevant for OD2-theory.Comment: 24 pages, Latex. v2:Sections 3.2 and 3.3 improved. v3:Some clarifications added. Version published in JHE

Supersymmetric Deformations of Maximally Supersymmetric Gauge Theories

We study supersymmetric and super Poincar\'e invariant deformations of ten-dimensional super Yang-Mills theory and of its dimensional reductions. We describe all infinitesimal super Poincar\'e invariant deformations of equations of motion of ten-dimensional super Yang-Mills theory and its reduction to a point; we discuss the extension of them to formal deformations. Our methods are based on homological algebra, in particular, on the theory of L-infinity and A-infinity algebras. The exposition of this theory as well as of some basic facts about Lie algebra homology and Hochschild homology is given in appendices.Comment: New results added. 111 page

The Seven-sphere and its Kac-Moody Algebra

We investigate the seven-sphere as a group-like manifold and its extension to a Kac-Moody-like algebra. Covariance properties and tensorial composition of spinors under $S^7$ are defined. The relation to Malcev algebras is established. The consequences for octonionic projective spaces are examined. Current algebras are formulated and their anomalies are derived, and shown to be unique (even regarding numerical coefficients) up to redefinitions of the currents. Nilpotency of the BRST operator is consistent with one particular expression in the class of (field-dependent) anomalies. A Sugawara construction is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files appende

The general classical solution of the superparticle

The theory of vectors and spinors in 9+1 dimensional spacetime is introduced in a completely octonionic formalism based on an octonionic representation of the Clifford algebra \Cl(9,1). The general solution of the classical equations of motion of the CBS superparticle is given to all orders of the Grassmann hierarchy. A spinor and a vector are combined into a $3 \times 3$ Grassmann, octonionic, Jordan matrix in order to construct a superspace variable to describe the superparticle. The combined Lorentz and supersymmetry transformations of the fermionic and bosonic variables are expressed in terms of Jordan products.Comment: 11 pages, REVTe

D3-brane action in a supergravity background: the fermionic story

Using the kappa-symmetric action for a D3-brane, we study the interaction between its world-volume fermions and a bosonic type IIB supergravity background preserving 4-dimensional Lorentz invariance. We find that the renormalizable terms in the action include only coupling between the fermions and the 3-form flux in the combination *G_3-iG_3, which is zero for a class of supersymmetric and nonsupersymmetric solutions. We also find the magnetic and electric dipole moments for the fermions, which are proportional to the derivative of the dilaton-axion. We show that different gauges to fix the kappa-symmetry give the same interaction terms, and prove that these terms are also SL(2,R) self-dual. We interpret our results in terms of N=1 supersymmetric gauge theory on the D-brane.Comment: 23 pages. Minor corrections, references adde

Regular solutions to higher order curvature Einstein--Yang-Mills systems in higher dimensions

We study regular, static, spherically symmetric solutions of Yang-Mills theories employing higher order invariants of the field strength coupled to gravity in $d$ dimensions. We consider models with only two such invariants characterised by integers $p$ and $q$. These models depend on one dimensionless parameter $\alpha$ leading to one-parameter families of regular solutions, obtainable by numerical solution of the corresponding boundary value problem. Much emphasis is put on an analytical understanding of the numerical results.Comment: 34 pages, 12 figure

Yang--Mills sphalerons in all even spacetime dimensions d=2kd=2k, k>2k>2 : kk=3,4

The classical solutions to higher dimensional Yang--Mills (YM) systems, which are integral parts of higher dimensional Einstein--YM (EYM) systems, are studied. These are the gravity decoupling limits of the fully gravitating EYM solutions. In odd spacetime dimensions, depending on the choice of gauge group, these are either topologically stable or unstable. Both cases are analysed, the latter numerically only. In even spacetime dimensions they are always unstable, describing saddle points of the energy, and can be described as {\it sphalerons}. This instability is analysed by constructing the noncontractible loops and calculating the Chern--Simons (CS) charges, and also perturbatively by numerically constructing the negative modes. This study is restricted to the simplest YM system in spacetime dimensions $d=6,7,8$, which is amply illustrative of the generic case.Comment: 16 pages, 3 figures ; comments added, to appear in J. Phys.

Higher Derivative Corrections to Eleven Dimensional Supergravity via Local Supersymmetry

In this paper we derive higher derivative corrections to the eleven dimensional supergravity by applying the Noether method with respect to the N=1 local supersymmetry. An ansatz for the higher derivative effective action, which includes quartic terms of the Riemann tensor, is parametrized by 132 parameters. Then we show that by the requirement of the local supersymmetry, the higher derivative effective action is essentially described by two parameters. The bosonic parts of these two superinvariants completely match with the known results obtained by the perturbative calculations in the type IIA superstring theory. Since the calculations are long and systematic, we build the computer programming to check the cancellation of the variations under the local supersymmetry. This is an extended version of our previous paper hep-th/0508204.Comment: 67 pages, no figure, references added, typos correcte