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.     

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.     

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.     

Spontaneous breaking of supersymmetry and gauge invariance in supergravity

Using the new minimal auxiliary fields of N = 1 supergravity it is found possible to construct a model of local supersymmetry which spontaneously breaks both supersymmetry and gauge invariance. The status of the cosmological constant resulting from this breaking is discussed.     

Two-charged non-extremal rotating black holes in seven-dimensional gauged supergravity: The single-rotation case

We construct the solution for non-extremal charged rotating black holes in seven-dimensional gauged supergravity, in the case with only one rotation parameter and two independent charges. Using the Boyer-Lindquist coordinates, the metric is expressed in a generalized form of the ansatz previously presented in [S.Q. Wu, Phys. Rev. D 83 (2011) 121502(R)], which may be helpful to find the most general non-extremal two-charged rotating black hole with three unequal rotation parameters. The conserved charges for thermodynamics are also computed.     

One-loop Kähler potential in 5D gauged supergravity with generic prepotential

We calculate one-loop contributions to the Kähler potential in 4D effective theory of 5D gauged supergravity (SUGRA) on S¹/_Z2$S^1/Z_2$ with a generic form of the prepotential   and arbitrary boundary terms. Our result is applicable to a wide class of 5D SUGRA models. The derivation is systematically performed by means of an N=1$N=1$ superfield formalism based on the superconformal formulation of 5D SUGRA. As an illustrative example, we provide an explicit expression of the Kähler potential in the case of 5D flat spacetime.     

U(N) invariance in extended supergravity

U(N) invariance of previously established extended supergravity theories (O(1), O(2), O(3)) is shown to be also compatible with the O(4) theory at the first non-trivial order in the Newton constant. If U(4) invariance remains true to all orders the non-polynomial feature of this theory is enormously simplified. As an example we determine, to all orders, the non-polynomial correction to the spin-1 kinetic term using some of the constraints of supersymmetry.     

Extended supergravity with local SO(5) invariance

We present a version of N = 5 supergravity with local SO(5) invariance and a lowest order calculation for N = 8 supergravity with local SO(8). The implications of these results and related aspects are discussed.     

The inflationary universe in the gauged N=8 supergravity induced from a superstring

N=8 supergravity can contain a large negative cosmological constant. If this supergravity was induced on a four-dimensional space-time submanifold of a ten-dimensional space by a superstring moving in the latter manifold then there exists the possibility of a mutual cancellation of the constant mentioned and a positive one arising on the given submanifold due to quantum effects from the superstring. After this the evolution of the submanifold will depend essentially on its topological properties.