K. Pilch

Self-duality in odd dimensions

Abstract For spacetime dimension d = 4 k − 1 one may take the “square root” of the Proca equation for a massive antisymmetric tensor field. The result is a “self-dual” field which propagates half as many massive modes. We present a simple supersymmetric model for d = 3. We also discuss other types of odd-dimensional self-duality, in d = 4 k + 1 and in euclidean spaces.

Gauged N=8 d=5 supergravity

Abstract The complete gauged nonlinear N = 8 d = 5 supergravity action and supersymmetry transformation laws (without four- and three-fermion terms) are presented. They are obtained from the ungauged model by reinterpreting part of the field strenghts of the abelian vector fields as real self-dual second-rank antisymmetric tensors. The complete set of T-tensor identities are given and their validity is checked numerically. The model has a local Yang-Mills SO(6) and a local composite USp(8) symmetry. The self-duality is essential for the consistent coupling of the antisymmetric tensors to the nonabelian gauge fields.

Compactification of d = 11 supergravity on S4 (or 11 = 7 + 4, too)

Abstract Eleven-dimensional supergravity can compactify spontaneously on either S 7 or S 4 . We study the latter case, with attention to its connection with a possible gauged N = 4 supergravity in d = 7. We derive the linearized field equations and supersymmetry transformation rules for the effective d = 7 supergravity multiplet. There are five third rank antisymmetric tensors in this multiplet which are in the 5 representation of the gauge group USp(4) and they are propagated with a self-duality condition in 7 dimensions . There is also a 14 of scalar fields and they are found to propagate with a non -conformal wave operator.

De Sitter superalgebras and supergravity

A general analysis of all possible super-extensions of anti-de Sitter and de Sitter algebrasO(3, 2) andO(4, 1) is presented. It is shown that actions with de Sitter local supersymmetry exist, but contain vector-ghosts.

Gauging of d = 11 supergravity

The role of antisymmetric tensor fields in the gauging of groups is related to theorems on cohomology theory, and Cartan integrable systems are discussed. Examples are given. Various possibilities to gauge d = 11 supergravity by decontracting its underlying group are considered. In particular the simple supergroups Osp (1Vertical Bar64) and SU(32Vertical Bar1) yield a negative result, but a certain non-semisimple supergroup containing Osp(1Vertical Bar32) is proposed as a viable candidate. The corresponding action would no longer contain the 3-index photon A/sub munurho/, but instead a second spin (3)/(2) field eta/sub ..mu../ and boson fields B..mu../sup a//sub 1/a/sub 2/ and B..mu../sup a//sub 1/xxxa/sub 5/. A first order formalism for d = 11 is presented. It is to be used for an improved form of dimensional reduction.

Noncompact Gaugings and Critical Points of Maximal Supergravity in Seven-dimensions

From the recently obtained SO(5)-gauged maximal d = 7 supergravity, we derive further noncompact SO(4, 1) and SO(3, 2) gaugings. Their potentials have no critical points. The SO(5) potential has two critical points with SO(5) and SO(4) symmetry, respectively. The former is stable under small and large fluctuations, the latter is unstable and breaks all supersymmetries.

Fermion spectra from superstrings

Abstract Some compactifications of the ten-dimensional anomaly-free E 8 × E 8 and SO(32) theories that correspond to superstrings are studied. Compactification is achieved by setting the classical gauge field equal to the spin connection. The resulting chiral fermion spectra are obtained for any six-dimensional manifold, under the condition Tr F 2 = 30 Tr R 2 , plus a quantization condition for U(1) charges. For E 8 × E 8 these conditions lead to potentially realistic models for any irreducible six-dimensional manifold and any embedding of the holonomy group. Apart from a few more exotic examples, the four-dimensional models we obtain are more or less standard SU(5), SO(10), SU(4) × SU(2) × SU(2) or E 6 models.

A minimal covariant action for the free open spinning string field theory

Abstract The BRST transformations of the string fields of the free open spinning string is analyzed. After expanding the string fields into ghost zero modes the BRST transformations are diagonalized and it is found that in the Ramond sector the physical fields are contained in only two string fields. A minimal covariant classical action for both sectors is constructed. The component expansion of the string fields yields the correct set of physical and Stueckelberg fields which are needed to construct a covariant local action for the corresponding massless and massive states. This is explicitly verified for the first three mass-levels.

Symmetric vacua of higher-dimensional Einstein-Yang-Mills theories

Abstract In the context of Kaluza-Klein compactification a general construction of symmetric solutions to the Einstein-Yang-Mills equations on isotropy irreducible coset spaces is given.

Do quarks know about Kähler metrics

Abstract We study compactification of ten-dimensional E 8 (×E 8 ) super-Yang-Mills theory on the coset manifold SU(3)/U(1) 2 . W obtain a three generation SO(10) model without mirror fermions. The internal space admits both Kahler and non-Kahler metrics, but the correct fermion mass spectrum can be obtained only if the metric is Kahler. In this case there is a natural mechanism for satisfying simultaneously the mass inequalities m t ≲ m W , m b ≪ m t and m u , m c ≪ t .