Constrained generalized supersymmetries and superparticles with tensorial central charges. A classification

We classify the admissible types of constraint (hermitian, holomorphic, with reality conditions on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. We further point out which constrained generalized supersymmetries admit a dual formulation. For both real and complex spinors generalized supersymmetries are constructed and classified as dimensional reductions of supersymmetries from {\em oxidized} space-times (i.e. the maximal space-times associated to $n$-component Clifford irreps). We apply these results to sistematically construct a class of models describing superparticles in presence of bosonic tensorial central charges, deriving the consistency conditions for the existence of the action, as well as the constrained equations of motion. Examples of these models (which, in their twistorial formulation, describe towers of higher-spin particles) were first introduced by Rudychev and Sezgin (for real spinors) and later by Bandos and Lukierski (for complex spinors).Comment: 32 pages, LaTe

Large Gauge Transformations in M-theory

We cast M-brane interactions including intersecting membranes and five-branes in manifestly gauge invariant form using an arrangement of higher dimensional Dirac surfaces. We show that the noncommutative gauge symmetry present in the doubled M-theory formalism involving dual 3-form and 6-form gauge fields is preserved in a form quantised over the integers. The proper context for discussing large noncommutative gauge transformations is relative cohomology, in which the 3-form transformation parameters become exact when restricted to the five-brane worldvolume. We show how this structure yields the lattice of M-theory charges and gives rise to the conjectured 7D Hopf-Wess-Zumino term.Comment: 45 pages, 9 figures, LaTe

The W3W_3-string spectrum

We study the spectrum of $W_3$ strings. 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 $d\ne26$ with anomalies cancelled by appropriate background charges. In the case of the $W_3$ string, however, the spin-two ``graviton'' is massive.Comment: 14 Page

BPS Branes in Supergravity

This review considers the properties of classical solutions to supergravity theories with partially unbroken supersymmetry. These solutions saturate Bogomol'ny-Prasad-Sommerfield bounds on their energy densities and are the carriers of the $p$-form charges that appear in the supersymmetry algebra. The simplest such solutions have the character of $(p+1)$-dimensional Poincaré-invariant hyperplanes in spacetime, i.e. $p$-branes. Topics covered include the relations between mass densities, charge densities and the preservation of unbroken supersymmetry; interpolating-soliton structure; diagonal and vertical Kaluza-Klein reduction families; multiple-charge solutions and the four D=11 elements; duality-symmetry multiplets; charge quantisation; low-velocity scattering and the geometry of worldvolume supersymmetric $\sigma$-models; and the target-space geometry of BPS instanton solutions obtained by the dimensional reduction of static $p$-branes.This review considers the properties of classical solutions to supergravity theories with partially unbroken supersymmetry. These solutions saturate Bogomol'ny-Prasad-Sommerfield bounds on their energy densities and are the carriers of the $p$-form charges that appear in the supersymmetry algebra. The simplest such solutions have the character of $(p+1)$-dimensional Poincar\'e-invariant hyperplanes in spacetime, i.e. $p$-branes. Topics covered include the relations between mass densities, charge densities and the preservation of unbroken supersymmetry; interpolating-soliton structure; diagonal and vertical Kaluza-Klein reduction families; multiple-charge solutions and the four D=11 elements; duality-symmetry multiplets; charge quantisation; low-velocity scattering and the geometry of worldvolume supersymmetric $\sigma$-models; and the target-space geometry of BPS instanton solutions obtained by the dimensional reduction of static $p$-branes

Weyl Group Invariance and p-brane Multiplets

In this paper, we study the actions of the Weyl groups of the U duality groups for type IIA string theory toroidally compactified to all dimensions $D\ge 3$. We show how these Weyl groups implement permutations of the field strengths, and we discuss the Weyl group multiplets of all supersymmetric $p$-brane solitons.Comment: 31 pages, Late

Embedding of the Bosonic String into the W3W_3 String

We investigate new realisations of the $W_3$ algebra with arbitrary central charge, making use of the fact that this algebra can be linearised by the inclusion of a spin-1 current. We use the new realisations with $c=102$ and $c=100$ to build non-critical and critical $W_3$ BRST operators. Both of these can be converted by local canonical transformations into a BRST operator for the Virasoro string with $c=28-2$, together with a Kugo-Ojima topological term. Consequently, these new realisations provide embeddings of the Virasoro string into non-critical and critical $W_3$ strings.Comment: 11 pages. (Some referencing changes

Covariant Pauli-Villars Regularization of Quantum Gravity at the One Loop Order

We study a regularization of the Pauli-Villars kind of the one loop gravitational divergences in any dimension. The Pauli-Villars fields are massive particles coupled to gravity in a covariant and nonminimal way, namely one real tensor and one complex vector. The gauge is fixed by means of the unusual gauge-fixing that gives the same effective action as in the context of the background field method. Indeed, with the background field method it is simple to see that the regularization effectively works. On the other hand, we show that in the usual formalism (non background) the regularization cannot work with each gauge-fixing.In particular, it does not work with the usual one. Moreover, we show that, under a suitable choice of the Pauli-Villars coefficients, the terms divergent in the Pauli-Villars masses can be corrected by the Pauli-Villars fields themselves. In dimension four, there is no need to add counterterms quadratic in the curvature tensor to the Einstein action (which would be equivalent to the introduction of new coupling constants). The technique also works when matter is coupled to gravity. We discuss the possible consequences of this approach, in particular the renormalization of Newton's coupling constant and the appearance of two parameters in the effective action, that seem to have physical implications.Comment: 26 pages, LaTeX, SISSA/ISAS 73/93/E

Generalised Holonomy for Higher-Order Corrections to Supersymmetric Backgrounds in String and M-Theory

The notion of {\it generalised structure groups} and {\it generalised holonomy groups} has been introduced in supergravity, in order to discuss the spinor rotations generated by commutators of supercovariant derivatives when non-vanishing form fields are included, with their associated gamma-matrix structures that go beyond the usual \Gamma_{MN} of the Riemannian connection. In this paper we investigate the generalisations to the usual Riemannian structure and holonomy groups that result from the inclusion of higher-order string or M-theory corrections in the supercovariant derivative. Even in the absence of background form fields, these corrections introduce additional terms \Gamma_{M_1... M_6} in the supercovariant connection, and hence they lead to enlarged structure and holonomy groups. In some cases, the corrected equations of motion force form fields to become non-zero too, which can further enlarge the groups. Our investigation focuses on the generalised structure and holonomy groups in the transverse spaces K_n of (Minkowski) \times K_n backgrounds for n=6, 7, 8 and 10, and shows how the generalised holonomies allow the continued existence of supersymmetric backgrounds even though the usual Riemannian special holonomy is destroyed by the inclusion of the string or M-theory corrections.Comment: Latex, 23 pages, clarifying comments and references adde

Supersymmetry counterterms revisited

Superspace power-counting rules give estimates for the loop order at which divergences can first appear in non-renormalisable supersymmetric field theories. In some cases these estimates can be improved if harmonic superspace, rather than ordinary superspace, is used. The new estimates are in agreement with recent results derived from unitarity calculations for maximally supersymmetric Yang-Mills theories in five and six dimensions. For N=8 supergravity in four dimensions, we speculate that the onset of divergences may correspondingly occur at the six loop order.Comment: 10 pages, plain Late

Higher dimensional gravity invariant under the Poincare group

It is shown that the Stelle-West Grignani-Nardelli-formalism allows, both when odd dimensions and when even dimensions are considered, constructing actions for higher dimensional gravity invariant under local Lorentz rotations and under local Poincar\`{e} translations. It is also proved that such actions have the same coefficients as those obtained by Troncoso and Zanelli in ref. Class. Quantum Grav. 17 (2000) 4451.Comment: 7 pages, Latex, accepted in Phys. Rev.