L.J. Romans

Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory

Abstract In asymptotically flat (AF) space, the extreme Reissner-Nordstrom (RN) black hole is distinguished by its coldness (vanishing Hawking temperature) and its supersymmetry. We examine RN solutions to Einstein-Maxwell theory with a cosmological constant Λ, classifying the cold black holes and, for positive Λ, the “lukewarm” black holes at the same temperature as the de Sitter thermal background. For negative Λ, we classify the supersymmetric solutions within the context of N = 2 gauged supergravity. One finds supersymmetric analogues of AF-space extreme RN black holes, which for nonzero Λ differ from the cold black holes. In addition, these is an exotic class of supersymmetric solutions which cannot be continued to asymptotically flat space, since the magnetic charge becomes infinite in that limit.

Compact and non-compact gauged supergravity theories in five dimensions☆

Abstract We give a detailed construction of gauged N = 8 supergravity theories in five dimensions with Yang-Mills gauge groups SO( p , 6− p )( p =0, 1, 2, 3), physical global symmetry SU(1, 1), and local composite symmetry USp(8). The scalar potentials are studied and several critical points are found for the SO(6) and SO(3,3) theories. Those of the SO(6) theory are related to compactifications of the chiral N = 2 theory in ten dimensions. We discuss truncations of the SO(6) theory and give an independent discussion of the relevant N = 2,4,6 and 8 anti-de Sitter supermultiplets.

Gauged N = 8 supergravity in five dimensions☆

Abstract We construct gauged N = 8 supergravity theories in five dimensions. Instead of the twenty-seven vector fields of the ungauged theory, the gauged theories contain fifteen vector fields and twelve second-rank antisymmetric tensor fields satisfying self-dual field equations. The fifteen vector fields can be used to gauge any of the fifteen-dimensional semisimple subgroups of SL(6, R ), specially SO( p , 6− p ) for p = 0, 1, 2, 3. The gauged theories also have a physical global SU(1,1) symmetry which survives from the E 6(6) symmetry of the ungauged theory. This SU(1,1) for the SO(6) gauging is presumably related to that of the chiral N = 2 theory in ten dimensions. In our formalism we maintain a composite local USp(8) symmetry analogous to SU(8) in four dimensions.

A classification of compactifying solutions for d =11 supergravity☆

Abstract Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail. The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry. The existence of a spin structure on homogeneous manifolds G H is discussed and related to topological properties of G H . As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.

New compactifications of Chiral N = 2, d = 10 supergravity☆

Abstract We present a number of new compactifying solutions of chiral N = 2 ten-dimensional supergravity to five dimensions. Several are of the standard Freund-Rubin type; we give a complete classification of such compactifications for which the internal space M 5 is a coset manifold. In another type of solution M 5 is a non-Einstein U(1) bundle over a four-dimensional Kahler space, and the complex three-index field strength is nonvanishing in the internal directions. The latter construction gives a solution with SU(3) symmetry when M 5 is taken to be a stretched five-sphere.

N = 3 and N = 1 supersymmetry in a new class of solutions for d = 11 supergravity☆

We present a new class of compactifying solutions for d = 11 supergravity. The internal 7-spaces are described by coset manifolds Npqr of the form SU(3) × U(1)/U(1) × U(1). The three integers p, q, r characterize the embedding of the stability subgroup U(1) × U(1) in SU(3) × U(1). Their supersymmetry content is quite remarkable. For a particular choice of p, q, r the isometry of Npqr is SU(3) × SU(2): in this case we find that N = 3 supersymmetry survives. For all the other values of p, q, r, supersymmetry is broken to N = 1, and the isometry group is SU(3) × U(1). We also find a class of solutions with internal photon curl Fαβγδ ≠ 0, breaking all supersymmetries.

The Super

We construct a higher-spin N = 2 superalgebra whose bosonic sector is W ∞ ⊕ W 1+∞ . It can be realised in terms of bilinear currents involving free complex bosonic and fermionic fields. We also discuss the spectral flow, and various truncations.

W

Abstract Known theorems about the isometry group of a general coset space G H are reviewed. The Killing vectors on G H are explicitly constructed. Rescalings of the coset vielbeins are discussed, and a simple criterion to find which rescalings preserve the isometry group is given. A general expression for the Riemann and Ricci tensors in terms of the rescaled vielbeins and the group structure constants is derived. These results have useful applications in Kaluza-Klein theories. As an example, the round and the squashed seven-spheres that have been used to compactify d = 11 supergravity are discussed, and it is shown that they can be identified with two appropriately rescaled coset spaces SO(5) SO(3) .

(infinity) Algebra

Abstract We determine some of the terms that must be added to the action of N = 1 supergravity coupled to N = 1 Yang-Mills theory in ten dimensions, if the Lorentz Chern-Simons term is included in the definition of the H mnp field strength, and supersymmetry is to be preserved. Amongst the new terms, we find that one has squares of the curvature tensors appearing in precisely the linear combinations suggested by other authors. We rewrite the theory in a geometrically suggestive form suitable for interpreting H mnp as a torsion tensor. We also comment on the relevance of this work to compactification on Calabi-Yau spaces.

Symmetries of coset spaces and Kaluza-Klein supergravity☆

Abstract We study the spectrum of W 3 string. In particular, we show that for appropriately chosen space-time signature, one of the scalar fields is singled out by the spin-3 constraint and is “frozen”: no creation operators from it can appear in physical states and the corresponding momentum must assume a specific fixed value. The remaining theory is unitary and resembles an ordinary string theory in d ≠ 26 with anomalies cancelled by appropriate background charges.