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).     

N = 3 and N = 1 supersymmetry in a new class of solutions for d = 11 supergravity

We present a new class of compactifying solutions for d = 11 supergravity. The internal 7-spaces are described by coset manifolds N^pqr of the form SU(3) × U(1)/U(1) × U(1). The three integers p, q, r characterize the embedding of the stability subgroup U(1) × U(1) in SU(3) × U(1).Their supersymmetry content is quite remarkable. For a particular choice of p, q, r the isometry of N^pqr is SU(3) × SU(2): in this case we find that N = 3 supersymmetry survives. For all the other values of p, q, r, supersymmetry is broken to N = 1, and the isometry group is SU(3) × U(1).We also find a class of solutions with internal photon curl F_αβγδ ≠ 0, breaking all supersymmetries.     

Use of compensators to break supersymmetry in an N = 1 supergravity theory

We consider an N = 1 supergravity theory with multiple compensators and show that supersymmetry is broken by a solution to the equation of motion of a compensator. When a chiral scalar superfield is coupled to supergravity, we discuss various aspects of supersymmetry breaking and show that the super-Higgs-Kibble effect is operative. Possible applications of this mechanism of supersymmetry breaking in model building and extended supergravity theories are indicated.     

The spontaneous breaking of supersymmetry in curved space-time

The spontaneous breaking of supersymmetry in the presence of a cosmological constant Λ is discussed in a class of theories that includes gauged supergravity and the recently constructed model of N = 1 supergravity coupled to supermatter. The stability of de Sitter, anti-de Sitter and Minkowski vacua in these theories is investigated. Positivity of energy is demonstrated in a model independent way for supersymmetric vacua, even if the scalar potential is unbounded below, and for global minima of the potential for Λ ? 0.Free fields in anti-de Sitter space are considered and the distinction made between the coefficients of quadratic terms in the lagrangian, which vanish for Goldstone scalars, and the physical masses, which give the frequencies and total energies of modes. The number of degrees of freedom depends on gauge invariance, not on the vanishing of mass.The one-loop corrections to the cosmological constant are given for Λ ? 0 and they vanish if the physical masses obey certain sum rules. It is, however, the bilinear coefficients in the N = 1 supergravity-supermatter lagrangian, rather than the physical masses, that satisfy a quadratic sum rule. This sum rule depends on Λ so that a given mass splitting can be obtained for arbitrarily large supersymmetry breaking scales if Λ is sufficiently large and negative.     

Supersymmetry breaking for the observable sector in superstring models

We discuss the supersymmetry breaking in four-dimensional supergravity models from superstrings including perturbative or non-perturbative string σ-model corrections. It is found that various soft supersymmetry breaking terms can appear with values of the order ofm _3/2 even at the tree level of effective field theory and of string theory.     

A grand unified theory based onSU(n, 1)-minimal supergravity

We discuss a grand unified theory in the framework ofSU(n, 1) minimal supergravity with the Planck mass as the only input mass scale.M _W ≈m _3/2 is fixed by radiative corrections to be naturally ?M _P1. Due to the particular form of explicit soft supersymmetry breaking a light singlet can be used to obtain naturally light Higgs doublets and for a new mechanism for radiativeSU (2)×U(1) breaking. The low energy particle spectrum is very restricted withm _3/2≈10⁴ GeV.     

Relating the CMSSM and SUGRA models with GUT-scale and super-GUT-scale supersymmetry breaking

While the constrained minimal supersymmetric standard model (CMSSM) with universal gaugino masses, m _1/2, scalar masses, m ₀, and A-terms, A ₀, defined at some high energy scale (usually taken to be the GUT scale) is motivated by general features of supergravity models, it does not carry all of the constraints imposed by minimal supergravity (mSUGRA). In particular, the CMSSM does not impose a relation between the trilinear and bilinear soft supersymmetry breaking terms, B ₀=A ₀?m ₀, nor does it impose the relation between the soft scalar masses and the gravitino mass, m ₀=m _3/2. As a consequence, tanβ is computed given values of the other CMSSM input parameters. By considering a Giudice–Masiero (GM) extension to mSUGRA, one can introduce new parameters to the Kähler potential which are associated with the Higgs sector and recover many of the standard CMSSM predictions. However, depending on the value of A ₀, one may have a gravitino or a neutralino dark matter candidate. We also consider the consequences of imposing the universality conditions above the GUT scale. This GM extension provides a natural UV completion for the CMSSM.     

Radiative gauge symmetry breaking in supersymmetric flipped SU(5)

The radiative breaking of the SU(5)×U(1) symmetry in the flipped SU(5) model recently proposed by Antoniadis et al. is studied using renormalization group techniques. It is shown that gaugino masses can only be the dominant source of supersymmetry breaking at the Planck scale if the U(1) gaugino mass M₁ is at least 10 times larger than the SU(5) gaugino mass M₅. If M₁≅M₅ at the Planck scale, non-vanishing trilinear soft breaking terms (“A-terms”) are needed already at the Planck scale. In both cases consequences for the sparticle spectrum at the weak scale are discussed.     

Proton decay in locally supersymmetric GUT

Proton decay is studied in the supergravity model with “the hidden sector” as the source of supersymmetry breaking. Each dimension-five operator is found to accompany ΔB ≠ 0 four-scalar interactions. The Higgs fermion exchange for loop diagrams at low energies can be as important as the gauge fermion exchange, if the associated Yukawa coupling is significant as suggested by the radiatively induced SU(2) × U(1) breaking mechanism. The experimental bound for p → K⁰μ⁺ gives the lower bound of the order of 10¹⁶ GeV for the mass of the baryon-number violating Higgs particle.     

Symmetry breaking in a supersymmetric model of strong and electroweak interactions

We describe a supersymmetric model of strong and electroweak interactions based on the gauge groupSU(3)×SU(2)×U(1)×?(1). We concentrate on the pattern of the spontaneous symmetry breaking by the tree level scalar potential. It is possible to break the?(1) factor at superlarge energies relative to the simultaneous breaking scale ofSU(2)×U(1) and supersymmetry. The model has?(1) anomalies. Attempts to make an anomaly-free model based on the groupE ₆ are described. We also comment on possible modifications of the?(1) anomaly problem due to gravitational effects.     

A natural solution to the μ-problem in supergravity theories

We propose a “natural” way to avoid the introduction by hand of a small mass scale μ in the observable sector of N = 1 supergravity theories. In our approach, μ automatically arises from the general couplings of broken supergravity. In this way, all low energy mass parameters arise only from supergravity breaking and, in particular, SU (2) × U (1) is left unbroken in the limit of exact supersymmetry. Our solution of the μ-problem presents interesting connections with the strong CP puzzle through the implementation of symmetriesàla Peccei and Quinn.     

Light singlet particles and their cosmological consequences in witten-type supersymmetric models

In a class of supersymmetric gauge models which generate a large mass scale from a supersymmetry breaking mass scale M through loop corrections, there exists generally a very light scalar particle which transforms like a singlet under SU(3)_c × SU(2)_L with no U(1) charge. Cosmological constraints on such a particle are so severe that an upper bound is set on possible values of supersymmetry breaking scale in this class of models as M ? 500 TeV provided that the large mass scale is 10¹⁵ GeV and the mass of the light scalar particle is generated in one-loop order. This bound holds even if the goldstino is not absorbed into the gravitino.     

The parallelizing S7 torsion in gauged N=8 supergravity

Using the parallelizing S⁷ torsion as an ansatz we investigate two solutions of gauged N=8 supergravity with SO(7) invariance. Supersymmetry is uniformly broken. We calculate the masses for these solutions which are both unstable. Certain apparent discrepancies with the results obtained by spontaneous compactification of d=11 supergravity are discussed. We establish that the compactification on the parallelized S⁷ has an SO(7) invariance and clarify the issue of supersymmetry breaking. The lack of stability in d=4 indicates that this d=11 solution is unstable.     

RG-invariant sum rule in a generalization of anomaly-mediated SUSY-breaking models

We study a generalization of anomaly-mediated supersymmetry-breaking (AMSB) scenarios, under the assumption that the effects of the high-scale theory do not completely decouple and that D-term type contributions can therefore be present. We investigate the effect of such possible D-term additional contributions to soft scalar masses by requiring that, for non-vanishing, renormalizable Yukawa couplings Y^ijk, the sum of squared soft supersymmetry breaking mass parameters, M²_ijk≡m_i²+m_j²+m_k², is RG-invariant, in the sense that it becomes independent of the specific ultraviolet boundary conditions as it occurs in the AMSB models. This type of models can avoid the problem of tachyonic solutions for the slepton mass spectrum present in AMSB scenarios. We implement the electroweak symmetry breaking condition and explore the sparticle spectrum associated with this framework. To show the possible diversity of the sparticle spectrum, we consider two examples, one in which the D-terms induce a common soft supersymmetry breaking mass term for all sfermion masses, and another one in which a light stop can be present in the spectrum.     

Effective super-Higgs and Str M2 from four-dimensional strings

We introduce supersymmetry breaking terms into the superpotential of the supergravity theories recently derived as the point field limit of the four-dimensional N = 1 superstrings. The terms we discuss have the special feature of giving mass to the gravitino without inducing one-loop quadratic divergences in the effective theory. It is shown that this property of the effective theory is due to the special geometrical structure shared by the scalar Kähler manifolds of the four-dimensional superstring-induced models.     

Superunification from eleven dimensions

We show how N = 8 supersymmetry can break spontaneously to N = 1 at the Planck scale via a Kaluza-Klein compactification of d = 11 supergravity on the squashed seven-sphere. Features unique to Kaluza-Klein supergravity are (i) the massless gravitino of the N = 1 phase comes from a massiveN = 8 supermultiplet, (ii) the scalars developing nonzero VEVs also belong to massive N = 8 supermultiplets, (iii) parity remains unbroken when N = 8 breaks to N = 1.Next we ask whether the resulting N = 1 theory can provide a realistic SU(3) × SU(2) × U(1) unification and speculate that it might if some of the gauge bosons and fermions are composite as in the EGMZ model. In contrast to their model, however, we avoid unwanted helicities and problems with their non-compact E₇. Moreover, we suggest a scheme in which the electroweak SU(2) × U(1) is a subgroup of the d = 11 general coordinate group but that the strong SU(3) is a subgroup of the d = 11 local Lorentz group and are not, therefore, to be combined into a GUT. The special properties of the seven-sphere also suggest a possible solution of the cosmological constant problem involving fermion condensates.     

Dynamics of O(N) chiral supersymmetry at finite energy density

We consider an O(N) version of a massive, interacting, chiral supersymmetry model solved exactly in the large N limit. We demonstrate that the system approaches a stable attractor at high energy densities, corresponding to a non-perturbative state for which the relevant field quanta are massless. The state is one of spontaneously broken O(N), which, due to the influence of supersymmetry, does not become restored at high energies. Introducing soft supersymmetry breaking to the Lagrangian results in scalar masses at the soft breaking scale m_s independent of the mass scale of supersymmetry μ, with even smaller masses for the fermions.     

Unified field theories with U(N) internal symmetries: G

Gauge theories for extended SU(N) conformal supergravity are constructed which are invariant under local scale, chiral, proper conformal, supersymmetry and internal SU(N) transformations. The relation between intrinsic parity and symmetry properties of their generators of the internal vector mesons is established. These theories contain no cosmological constants, but technical problems inherent to higher derivative actions are pointed out.     

No-scale supersymmetric GUTs

We construct locally supersymmetric GUTs in which radiative corrections determine all the mass scales which are hierarchically smaller than the Planck mass: $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{=}\text{O}\text{(m}{}_{\mathrm{<mtext>W</mtext>}}\text{) =}\text{exp}\text{(}\text{?}\text{O}\text{(1)}\text{α}{}_{\mathrm{<mtext>t</mtext>}}\text{)m}{}_{\mathrm{<mtext>p</mtext>}}$, etc. Such no-scale GUTs are based on a hidden sector with a flat potential guaranteed by SU(1, 1) conformal invariance. This is extended to include observable chiral fields in an SU(n, 1)/SU(n) × U(1) structure reminiscent of N ? 5 extended supergravity theories. Tree-level supersymmetry breaking is present only for the gravitino, and for the light gaugino masses through non-minimal kinetic terms reminiscent of N?4 extended supergravity theories. Radiative corrections generate squark and slepton masses which are phenomenologically acceptable, and the right value of m_W is obtained if m_t ≈ 50 GeV in the simplest such model.     

Chiral-limit theorems and corrections to PCAC in a model for the scalar Kℓ3 divergence form factor

Three sum rules on vertex functions are derived by applying a model on two-particle Kπ channels. SU(3) × SU(3) breaking is introduced by corrections to the PCAC forms of the axial currents. Taking the m_π → 0 limit the sum rules reduce to the Callan-Treiman theorem, a recent theorem by Dashen, Li, Pagels and Weinstein (DLPW) and a third relation. We encounter non-analytic correction terms in the two first sum rules. In the DLPW theorem we find, contrary to a previous suggestion, non-negligible ε and ε²ln ε terms which are due to the large K-mass. These terms are responsible for a curvature of the scalar K_?3 form factor, however negative values of the slope at the origin require also substantial SU(2) × SU(2) violations. The numerical results taking into account physical masses compare favourably with K_?3 decay and also with s-wave Kπ scattring data.