De Sitter Space in Supergravity and M Theory

Two ways in which de Sitter space can arise in supergravity theories are discussed. In the first, it arises as a solution of a conventional supergravity, in which case it necessarily has no Killing spinors. For example, de Sitter space can arise as a solution of N=8 gauged supergravities in four or five dimensions. These lift to solutions of 11-dimensional supergravity or D=10 IIB supergravity which are warped products of de Sitter space and non-compact spaces of negative curvature. In the second way, de Sitter space can arise as a supersymmetric solution of an unconventional supergravity theory, which typically has some kinetic terms with the `wrong' sign; such solutions are invariant under a de Sitter supergroup. Such solutions lift to supersymmetric solutions of unconventional supergravities in D=10 or D=11, which nonetheless arise as field theory limits of theories that can be obtained from M-theory by timelike T-dualities and related dualities. Brane solutions interpolate between these solutions and flat space and lead to a holographic duality between theories in de Sitter vacua and Euclidean conformal field theories. Previous results are reviewed and generalised, and discussion is included of Kaluza-Klein theory with non-compact internal spaces, brane and cosmological solutions, and holography on de Sitter spaces and product spaces.Comment: Referneces added, 36 page

Matrix Theory, U-Duality and Toroidal Compactifications of M-Theory

Using U-duality, the properties of the matrix theories corresponding to the compactification of M-theory on $T^d$ are investigated. The couplings of the $d+1$ dimensional effective Super-Yang-Mills theory to all the M-theory moduli is deduced and the spectrum of BPS branes in the SYM gives the corresponding spectrum of the matrix theory.Known results are recovered for $d\le 5$ and predictions for $d>5$ are proposed. For $d>3$, the spectrum includes $d-4$ branes arising from YM instantons, and U-duality interchanges momentum modes with brane wrapping modes.For $d=6$, there is a generalised $\th$-angle which couples to instantonic 3-branes and which combines with the SYM coupling constant to take values in $SL(2,\R)/U(1)$, acted on by an $SL(2,\Z)$ subgroup of the U-duality group $E_6(\Z)$. For $d=4,7,8$, there is an $SL(d+1)$ symmetry, suggesting that the matrix theory could be a scale-invariant $d+2$ dimensional theory on $T^{d+1} \times \R$ in these cases, as is already known to be the case for $d=4$; evidence is found suggesting this happens for $d=8$ but not $d=7$.Comment: 28 Pages, Phyzzx Macro. Minor correction

U-Duality and BPS Spectrum of Super Yang-Mills Theory and M-Theory

It is shown that the BPS spectrum of Super-Yang-Mills theory on $T^d\times \R$, which fits into representations of the U-duality group for M-theory compactified on $T^{d}$, in accordance with the matrix-theory conjecture, in fact fits into representations of the U-duality group for M-theory on $T^{d+1}$, the extra dualities realised as generalised Nahm transformations. The spectrum of BPS M-branes is analysed, new branes are discussed and matrix theory applications described.Comment: 18 Pages, Tex, Phyzzx Macro. References added, minor correction

Manifestly Covariant Actions for D=4 Self-Dual Yang-Mills and D=10 Super-Yang-Mills

Using an infinite number of fields, we construct actions for D=4 self-dual Yang-Mills with manifest Lorentz invariance and for D=10 super-Yang-Mills with manifest super-Poincar\'e invariance. These actions are generalizations of the covariant action for the D=2 chiral boson which was first studied by McClain, Wu, Yu and Wotzasek.Comment: Removed an unnecessary term from the super-Yang-Mills action and added a reference. 12 pages harvmac te

Singular Contractions of W-algebras

Many $W$-algebras (e.g. the $W_N$ algebras) are consistent for all values of the central charge except for a discrete set of exceptional values. We show that such algebras can be contracted to new consistent degenerate algebras at these exceptional values of the central charge.Comment: 10 pages, phyzzx.tex, QMW-92-7.(minor spelling and acknowledgement corrections

New Gauged N=8, D=4 Supergravities

New gaugings of four dimensional N=8 supergravity are constructed, including one which has a Minkowski space vacuum that preserves N=2 supersymmetry and in which the gauge group is broken to $SU(3)xU(1)^2$. Previous gaugings used the form of the ungauged action which is invariant under a rigid $SL(8,R)$ symmetry and promoted a 28-dimensional subgroup ($SO(8),SO(p,8-p)$ or the non-semi-simple contraction $CSO(p,q,8-p-q)$) to a local gauge group. Here, a dual form of the ungauged action is used which is invariant under $SU^*(8)$ instead of $SL(8,R)$ and new theories are obtained by gauging 28-dimensional subgroups of $SU^*(8)$. The gauge groups are non-semi-simple and are different real forms of the $CSO(2p,8-2p)$ groups, denoted $CSO^*(2p,8-2p)$, and the new theories have a rigid SU(2) symmetry. The five dimensional gauged N=8 supergravities are dimensionally reduced to D=4. The $D=5,SO(p,6-p)$ gauge theories reduce, after a duality transformation, to the $D=4,CSO(p,6-p,2)$ gauging while the $SO^*(6)$ gauge theory reduces to the $D=4, CSO^*(6,2)$ gauge theory. The new theories are related to the old ones via an analytic continuation. The non-semi-simple gaugings can be dualised to forms with different gauge groups.Comment: 33 pages. Reference adde