Stability of gravity with a cosmological constant

The stability properties of Einstein theory with a cosmological constant Λ are investigated. For Λ > 0, stability is established for small fluctuations, about the de Sitter background, occurring inside the event horizon and semiclassical stability is analyzed. For Λ < 0, stability is demonstrated for all asymptotically anti-de Sitter metrics. The analysis is based on the general construction of conserved flux-integral expressions associated with the symmetries of a chosen background. The effects of an event horizon, which lead to Hawking radiation, are expressedfor general field hamiltonians. Stability for Λ < 0 is proved, using supergravity techniques, in terms of the graded anti-de Sitter algebra with spinorial charges also expressed as flux integrals.     

Gauged N = 4 supergravities in five dimensions and their magnetovac backgrounds

Gauged N = 4 supergravity theories with Yang-Mills symmetry SU(2) × U(1) are constructed in five dimensions. As in four dimensions, the presence of a nonsimple gauge group leads to the existence of three distinct theories, depending (in five dimensions) on the values of the SU(2) and U(1) coupling constants. Two of the theories are distinguished by the relative sign of the coupling constants; one of these has a vacuum state exhibiting the full N = 4 anti-de Sitter supersymmetry SU(2,2|2), while the other has a scalar potential with no critical points. The third theory, in which the SU(2) coupling constant is taken to be zero, has vanishing scalar potential. This leads to vacua with spontaneously broken supersymmetry and zero cosmological constant, admitting compactification to four dimensions. All three theories possess “magnetovac” ground states with residual supersymmetry and hence presumably stable. Several of these may be interpreted as four-dimensional cosmological models.     

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.     

de Sitter vacua from matter superpotentials

Consistent uplifting of AdS vacua in string theory often requires extra light degrees of freedom in addition to those of a (Kähler) modulus. Here we consider the possibility that de Sitter and Minkowski vacua arise due to hidden sector matter interactions. We find that, in this scheme, the hierarchically small supersymmetry breaking scale can be explained by the scale of gaugino condensation and that interesting patterns of the soft terms arise. In particular, a matter-dominated supersymmetry breaking scenario and a version of the mirage mediation scheme appear in the framework of spontaneously broken supergravity.     

Two-dimensional higher-derivative supergravity and a new mechanism for supersymmetry breaking

We discuss the general form of quadratic (1,1) supergravity in two dimensions, and show that this theory is equivalent to two scalar supermultiplets coupled to nontrivial supergravity. It is demonstrated that the theory possesses stable vacua with vanishing cosmological constant which spontaneously break supersymmetry.     

Hidden constants: The θ parameter of QCD and the cosmological constant of N = 8 supergravity

For field theories that include the abelian gauge field A_μν? the field equations allow an arbitrary integration constant, which does not appear in the lagrangian but which does affect the physics. We present two applications: (i) the θ parameter of effective lagrangians for chiral symmetry breaking in QCD, and (ii) the cosmological constant in N = 8 supergravity, which does not require a gauging of the O(8) symmetry, but is rather due to a spontaneous breakdown of supersymmetry.     

One-loop effective potential in gauged O(4) supergravity and the problem of the Λ term

We calculate the one-loop, off-shell, effective action in O(4) gauged supergravity assuming an (anti) de Sitter metric and constant scalar fields as a background. The problem of the large induced Λ term (present already for free matter fields) is stressed and the possibility of dynamical breakdown of local supersymmetry is pointed out. We illustrate our techniques and qualitative conclusions on a number of examples, including Ø⁴ theory and QED scalar potentials on a de Sitter background and an effective action in Einstein theory with a cosmological constant. Possible solutions of the Λ-term problem are also discussed.     

Decoupling in supersymmetric theories

We examine the decoupling of massive states in supergravity theories. Using superspace functional techniques to “integrate out” the massive modes we derive the effective low-energy lagrangian. The technique is extended to the case of large supersymmetry breaking and we show how the effective lagrangian correctly accounts for vacuum expectation values of massive fields. We discuss the structure of effective theories following from the superstring in which the effects of Kaluza-Klein modes and states massive after intermediate scale breaking are included. It is shown in the case of large intermediate scale breaking the theory should possess discrete symmetries to protect light states from large supersymmetry breaking and we list the conditions for viable models.     

Supersymmetries and BPS configurations on anti-de Sitter space

We study supersymmetry breaking due to the presence of branes on anti-de Sitter space and obtain conditions for brane orientations not to break too many supersymmetries. Using the conditions, we construct a brane configuration corresponding to a baryon in large N gauge theory, and it is shown that the baryon is a marginal bound state of quarks, as is expected from supersymmetry.     

Some phenomenological implications of string loop effects

We investigate low energy implications of string loop corrections to supergravity couplings which break a possible flavor universality of the tree level. If supersymmetry is broken by the dilaton F-term, universal soft scalar masses arise at the leading order but string loop corrections generically induce flavor-non-diagonal soft terms. Constraints from flavor changing neutral currents (FCNC) and CP violation then require a large supersymmetry breading scale and thus heavy gluinos and squarks. If supersymmetry is broken by moduli F-terms, universality at the string tree level can only be guaranteed by extra conditions on the Kahler potential. A large hierarchy between the gluino and squark masses ensures that FCNC and CP-violation constraints are satisfied. If the soft scalar masses vanish at the string tree level, the cosmological problems related to light moduli can be evaded. However, generic string loop corrections violate FCNC bounds and require very heavy squark masses (∼ 100 TeV).     

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.     

Weak scale supersymmetry without weak scale supergravity

It is generally believed that weak scale supersymmetry implies weak scale supergravity, in the sense that the masses of the gravitino and gravitationally coupled moduli have masses below 100 TeV. This Letter presents a realistic framework for supersymmetry breaking in which these masses can be much larger. This solves the cosmological problems of hidden sector models. Supersymmetry breaking is communicated to the visible sector by anomaly-mediated supersymmetry breaking. The framework is compatible with perturbative gauge coupling unification and can be realized either in models of "warped" extra dimensions or in strongly coupled four-dimensional conformal field theories.     

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.     

Grand unification with local supersymmetry

We study general conditions for obtaining spontaneous breaking of local supersymmetry in N = 1 supergravity coupled to supersymmetric matter. We consider in particular the coupling of N = 1 supergravity to grand unified theories like SU(5) and study the conditions which must be met in order to obtain a realistic model. Specific models are built in which local supersymmetry is broken at a scale √M_Wm_p ～ 10¹⁰ GeV. This breaking of supersymmetry is only detected at low energies through soft terms breaking explicitly the global supersymmetry. These soft terms (scalar masses, gaugino masses and trilinear scalar couplings) are renormalized at low energies according to the renormalization group. The (mass)² of the Higgs doublet evolve towards negative values at low energies giving rise to SU(2) × U(1) breaking as a radiative effect of local supersymmetry breaking. We finally point out the possible relevance of non-renormalizable superpotentials for the problem of fermion masses.     

De Sitter universes and the emerging landscape in string theory

We discuss a recent proposal to construct de Sitter vacua in string theory. It is based on flux compactifications in string theory where all the moduli are stabilised and supersymmetry is broken with control. The resulting picture is that of a complicated landscape with many vacua of widely varying values for the cosmological constant.     

Semiclassical solutions ofOSp(N,4) supersymmetry 0

This work analyzes the connection between the so-called reflective boundary conditions and the spontaneous breaking of supersymmetry in anti-de Sitter background space. The one-loop effective potential of the Wess-Zumino model is computed using the supersymmetry invariant Pauli-Villars regularization procedure. The effect of the background geometry is determined exactly. It is shown that supersymmetry is preserved to the one-loop order at each classically supersymmetric extremum of the effective potential. Depending on the reflective boundary conditions chosen, quantum shifts in theA-field andB-field vacuum solutions are exhibited.     

A custodial symmetry for the cosmological constant in the effective theories of four-dimensional superstrings

We discuss supersymmetry breaking in the effective supergravity theories of four-dimensional N = 1 superstrings. Improving a recent suggestion, we introduce a superpotential modification that describes spontaneous supersymmetry breaking with vanishing cosmological constant and Str M² = 0 at any minimum of the tree level potential. We prove that in a class of models there are classical minima at which also Str f(M² = 0 for any function f. In particular, the whole one-loop cosmological constant vanishes. We propose a new boson-fermion symmetry of the spectrum, relating the graviton and the “dilatino”, which explains these remarkable properties.     

An alternative for moduli stabilisation

The one-loop vacuum energy is explicitly computed for a class of perturbative string vacua where supersymmetry is spontaneously broken by a T-duality invariant asymmetric Scherk–Schwarz deformation. The low-lying spectrum is tachyon-free for any value of the compactification radii and thus no Hagedorn-like phase-transition takes place. Indeed, the induced effective potential is free of divergence, and has a global anti-de Sitter minimum where geometric moduli are naturally stabilised.     

Nonlinear supergravity on a brane without compactification

We show that smooth domain wall spacetimes supported by a scalar field separating two anti-de Sitter-like regions admit a single graviton bound state. Our analysis yields a fully nonlinear supergravity treatment of the Randall-Sundrum model. Our solutions describe a pp-wave propagating in the domain wall background spacetime. If the latter is a Bogomol'nyi-Prasad-Sommerfeld state, our solutions retain some supersymmetry. Nevertheless, the Kaluza-Klein modes generate " pp curvature" singularities in the bulk located where the horizon of the anti-de Sitter region would ordinarily be.     

Compactification on non-symmetric six dimensional coset spaces with torsion

The equations of motion of a ten dimensional model based on the Chapline-Manton lagrangian, modified by higher derivative terms, are solved using six dimensional coset spaces with torsion. Minkowski space, anti-de Sitter, de Sitter and Einstein static cosmology with negative curvature are possible four dimensional cosmologies. In all case symmetry breaking schemesE ₈×E ₈→E ₈×E ₆ with chiral 27's ofE ₆ can be obtained.