Stability in gauged extended supergravity

Extended supergravity theories with gauged SO(N) internal symmetry have, for N ≥ 4, scalar field potentials which are unbounded below. Nevertheless, it is argued that the theories have ground states with anti-de Sitter background geometry which are stable against fluctuations which vanish sufficiently fast at spatial infinity. Stability is implied because the appropriate conserved energy functional is positive for such fluctuations. Anti-de Sitter space is not globally hyperbolic, but the boundary conditions required for positive energy are also shown to give free field theories with well-defined Cauchy problem. New information on the particle representations of OSp(1, 4) supersymmetry is presented as part of the argument. Supersymmetry requires boundary conditions for spin 0 fields such that only the improved stress tensor leads to a conserved energy functional. Although the stability arguments support the view that gauged supergravity theories are acceptable quantum field theories, the problem of a large cosmological term in the Ads phase of the theories is still unsolved.     

Maximal gauged supergravity in three dimensions

We construct maximally supersymmetric gauged N = 16 supergravity in three dimensions, thereby obtaining an entirely new class of anti--de Sitter supergravities. These models apparently cannot be derived from any known higher-dimensional theory and point to the existence of a new type of supergravity beyond D = 11. One of their noteworthy features is a non-Abelian generalization of the duality between scalar and vector fields in three dimensions. Among the possible gauge groups, SO(8) x SO(8) is distinguished as the maximal compact gauge group, but there are also more exotic possibilities such as F(4(-20)) x G2.     

Consistent spinor equations

Long-recognized curvature inconsistencies forS3/2 spinor equations are shown to result from an inconsistent transport law for the Infeld-Van der Waerden -symbols implied by conventional spinor derivatives. A curvature-free connection for the -symbols and a simple spinor form of the Levi-Civita connection for spinor fields yields consistent equations for any spin with no curvature restrictions.     

Magnetovacs in gauged N = 4 supergravity

A two-parameter family of supersymmetric background field solutions of the recently formulated version of gauged N = 4 supergravity is found. This constitutes strong evidence that the theory has stable vacua, despite energy densities that are unbounded below. The background geometries are metric products of (AdS)₂ × S₂, and there are covariantly constant magnetic and electric fields. For a special choice of parameters the (AdS)₂ factor becomes a flat Minkowski space and electric fields vanish.     

Supersymmetric AdS_4 vacua in N=3 gauged supergravity

We study the maximally supersymmetric AdS backgrounds of matter-coupled N=3 gauged supergravity in four dimensions. We find that to admit supersymmetric AdS vacua, the gauge group can only be of the form G_0×H?SO(3,n) with G_0 =SO(3),SO(3,1) or SL(3,R) and H a compact group of dimension n+3-dim(G_0). We also show that these AdS vacua have no moduli, namely they correspond to critical points in field space.     

General nonextremal rotating black holes in minimal five-dimensional gauged supergravity

We construct the general solution for nonextremal charged rotating black holes in five-dimensional minimal gauged supergravity. They are characterized by four nontrivial parameters: namely, the mass, the charge, and the two independent rotation parameters. The metrics in general describe regular rotating black holes, providing the parameters lie in appropriate ranges so that naked singularities and closed timelike curves (CTCs) are avoided. We calculate the conserved energy, angular momenta, and charge for the solutions, and show how supersymmetric solutions arise in a Bogomol'nyi-Prasad-Sommerfield limit. These have naked CTCs in general, but for special choices of the parameters we obtain new regular supersymmetric black holes or smooth topological solitons.     

Positive energy in anti-de Sitter backgrounds and gauged extended supergravity

The energy functional of a field theory with anti-de Sitter background geometry can be positive for scalar potentials which are unbounded below and for vacua corresponding to critical points which are maxima or saddle points.     

Anti-de Sitter BPS black holes in N=2 gauged supergravity

Electrically charged solutions breaking half of the supersymmetry in Anti-de Sitter four dimensional N=2 supergravity coupled to vector supermultiplets are constructed. These static black holes live in an asymptotic AdS₄ space time. The Killing spinor, i.e., the spinor for supersymmetry variation is explicitly constructed for these solutions.     

Uniqueness of rotating charged black holes in five-dimensional minimal gauged supergravity

We study a five-dimensional spacetime admitting, in the presence of torsion, a non-degenerate conformal Killing–Yano 2-form which is closed with respect to both the usual exterior differentiation and the exterior differentiation with torsion. Furthermore, assuming that the torsion is closed and co-closed with respect to the exterior differentiation with torsion, we prove that such a spacetime is the only spacetime given by the Chong–Cvetič–Lü–Pope solution for stationary, rotating charged black holes with two independent angular momenta in five-dimensional minimal gauged supergravity.     

Pure spinor integration from the collating formula

We use the technique developed by Becchi and Imbimbo to construct a well-defined BRST-invariant path integral formulation of pure spinor amplitudes. The space of pure spinors can be viewed from the algebraic geometry point of view as a collection of open sets where the constraints can be solved and a set of free and independent variables can be defined. On the intersections of those open sets, the functional measure jumps and one has to add boundary terms to construct a well-defined path integral. The result is the definition of the pure spinor integration measure constructed in terms of differential forms on each single patch.     

Instanton zero modes and β-functions in gauged supergravity

We prove that one loop infinities in N?3 gauged O(N) supergravities are produced only by zero modes both on de Sitter and gauge instanton backgrounds. This strongly suggests (in analogy with the super Yang-Mills case) that instantons may be used for establishing exact β-functions in supergravities. We also derive the general formula for the number of gauge instanton zero modes for arbitrary spin and find that the “magnetic moment” part of the contribution in the gauge β-function is completely due to zero modes.     

Pure type I supergravity and DE 10

We establish a dynamical equivalence between the bosonic part of pure type I supergravity in D = 10 and a D = 1 non-linear σ-model on the Kac–Moody coset space DE ₁₀/K(DE ₁₀) if both theories are suitably truncated. To this end we make use of a decomposition of DE ₁₀ under its regular SO(9,9) subgroup. Our analysis also deals partly with the fermionic fields of the supergravity theory and we define corresponding representations of the generalised spatial Lorentz group K(DE ₁₀).     

Nonlinear spinor equations in general relativity

General relativistic nonlinear spinor equations are proposed which reduce in the linear approximation to the Dirac equations, and in the slightly nonlinear approximation reduce to the Ivanenko - Heisenberg equations. When written in a vector form, the nonlinear spinor equations take the form of the Einstein equations, in which matter is produced by spinor fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 121–125, March, 1977.The author thanks professor D. D. Ivanenko for his support and a number of useful observations.     

On conformally covariant spinor field equations

A spinor field equation, covariant with respect to the general conformal group (including reflections), should consist in general of not less than eight linear equations and then, in Minkowski space, could be represented by not less than two massless Dirac equations. Their reduction through projectors to only one equation, while not spoiling conformal covariance implies unphysical consequences. It is shown instead that two Dirac equations may be brought unambiguously through a stereographic projection to a manifestly conformal covariant form inE _4,2 space. The physical implications are discussed and it is shown that if the fundamental elementary interactions are expressed in terms of conformal semispinors (which can never appear as free particles), then the corresponding physical Dirac spinors appear in the elementary interactions in terms of their chiral projections. This could indicate both the conformally invariant origin of weak interactions and their fundamental character. The possibility of constructing unified models from conformally invariant Lagrangians is envisaged.Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.A preliminary version was issued as Internal Report IC/78/43, ICTP Trieste May 1978, see also Lett. Nuovo Cim.21 (1978), 473.I am indebted to Prof. I. T.Todorov for interesting discussions.     

Bogomolny-type equations for gravitating gauged sigma models

It is shown that the complete set of field equations of a gauged sigma model coupled to gravity is satisfied by a set of first-order equations when the metric is static.     

Non-linear spinor equations with localized solutions

A method is outlined for finding non-linear spinor field equations which have stationary, localized solutions (solitons or droplets) of definite spin and parity.This work has been sponsored in part by the National Science Foundation, GF 42060