The role of singletons in S7S^7 compactifications

We derive the isometry irrep content of squashed seven-sphere compactifications of eleven-dimensional supergravity, i.e., the left-squashed ($LS^7$) with ${\mathcal N}=1$ and right-squashed ($RS^7$) with ${\mathcal N}=0$ supersymmetry, in a manner completely independent of the round sphere. Then we compare this result with the spectrum obtained by Higgsing the round sphere spectrum. This way we discover features of the spectra which makes it possible to argue that the only way the round spectrum can be related by a Higgs mechanism to the one of $LS^7$ is if the singletons are included in the round sphere spectrum. For this to work also in the $RS^7$ case it seems that the gravitino of the $LS^7$ spectrum must be replaced by a fermionic singleton present in the $RS^7$ spectrum.Comment: 24 pages including appendix with 12 figure, v2 minor typos correcte

The Low-level Spectrum of the W3W_3 String

We investigate the spectrum of physical states in the $W_3$ string theory, up to level 2 for a multi-scalar string, and up to level 4 for the two-scalar string. The (open) $W_3$ string has a photon as its only massless state. By using screening charges to study the null physical states in the two-scalar $W_3$ string, we are able to learn about the gauge symmetries of the states in the multi-scalar $W_3$ string.Comment: 31 pages, Plain Tex, CTP TAMU-70/92, Goteborg ITP 92-43, Imperial/TP/91-92/22, KCL-TH-92-

Holomorphic factorization of correlation functions in (4k+2)-dimensional (2k)-form gauge theory

We consider a free (2 k)-form gauge-field on a Euclidean (4 k + 2)-manifold. The parameters needed to specify the action and the gauge-invariant observables take their values in spaces with natural complex structures. We show that the correlation functions can be written as a finite sum of terms, each of which is a product of a holomorphic and an anti-holomorphic factor. The holomorphic factors are naturally interpreted as correlation functions for a chiral (2 k)-form, i.e. a (2 k)-form with a self-dual (2 k + 1)-form field strength, after Wick rotation to a Minkowski signature

Light-cone analysis of ungauged and topologically gauged BLG theories

We consider three-dimensional maximally superconformal Bagger-Lambert-Gustavsson (BLG) theory and its topologically gauged version (constructed recently in arXiv:0809.4478 [hep-th]) in the light-cone gauge. After eliminating the entire Chern-Simons gauge field, the ungauged BLG theory looks more conventional and, apart from the order of the interaction terms, resembles N=4 super-Yang-Mills theory in four dimensions. The light-cone superspace version of the BLG theory is given to quadratic and quartic order and some problems with constructing the sixth order interaction terms are discussed. In the topologically gauged case, we analyze the field equations related to the three Chern-Simons type terms of N=8 conformal supergravity and discuss some of the special features of this theory and its couplings to BLG.Comment: 22 pages; v2 some typos correcte

Generalised 11-dimensional supergravity

The low-energy effective dynamics of M-theory, eleven-dimensional supergravity, is taken off-shell in a manifestly supersymmetric superspace formulation. We show that a previously proposed relaxation of the torsion constraints can indeed accomodate a current supermultiplet. We comment on the relation and application of this completely general formalism to higher-derivative (R^4) corrections. This talk was presented by Bengt EW Nilsson at the Triangle Meeting 2000 ``Non-perturbative Methods in Field and String Theory'', NORDITA, Copenhagen, June 19-22, 2000, and by Martin Cederwall at the International Conference ``Quantization, Gauge Theory and Strings'' in memory of Efim Fradkin, Moscow, June 5-10, 2000

A Study of Holographic Renormalization Group Flows in d=6 and d=3

We present an explicit study of the holographic renormalization group (RG) in six dimensions using minimal gauged supergravity. By perturbing the theory with the addition of a relevant operator of dimension four one flows to a non-supersymmetric conformal fixed point. There are also solutions describing non-conformal vacua of the same theory obtained by giving an expectation value to the operator. One such vacuum is supersymmetric and is obtained by using the true superpotential of the theory. We discuss the physical acceptability of these vacua by applying the criteria recently given by Gubser for the four dimensional case and find that those criteria give a clear physical picture in the six dimensional case as well. We use this example to comment on the role of the Hamilton-Jacobi equations in implementing the RG. We conclude with some remarks on AdS_4 and the status of three dimensional superconformal theories from squashed solutions of M-theory.Comment: 15 pages, 5 figures, V2: minor change

Mass-Deformed BLG Theory in Light-Cone Superspace

Maximally supersymmetric mass deformation of the Bagger-Lambert-Gustavsson (BLG) theory corresponds to a {non-central} extension of the d=3 N=8 Poincare superalgebra (allowed in three dimensions). We obtain its light-cone superspace formulation which has a novel feature of the dynamical supersymmetry generators being {cubic} in the kinematical ones. The mass deformation picks a quaternionic direction, which breaks the SO(8) R-symmetry down to SO(4)xSO(4). The Hamiltonian of the theory is shown to be a quadratic form of the dynamical supersymmetry transformations, to all orders in the mass parameter, M, and the structure constants, f^{a b c d}.Comment: 23 page

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