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.     

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.     

FRW minisuperspace with local N=4 supersymmetry and self‐interacting scalar field

A supersymmetric FRW model with a scalar supermultiplet and generic superpotential is analysed from a quantum cosmological perspective. The corresponding Lorentz and supersymmetry constraints allow to establish a system of first order partial differential equations from which solutions can be obtained. We show that this is possible when the superpotential is expanded in powers of a parameter λ?1. At order λ⁰ we find the general class of solutions, which include in particular quantum states reported in the current literature. New solutions are partially obtained at order λ¹, where the dependence on the superpotential is manifest. These classes of solutions can be employed to find states for higher orders in λ. Our analysis further points to the following: (i) supersymmetric wave functions can only be found when the superpotential has either an exponential behaviour, an effective cosmological constant form or is zero; (ii) If the superpotential behaves differently during other periods, the wave function is trivial ( = 0, i.e., no supersymmetric states). We conclude this paper discussing how our FRW minisuperspace (with N = 4 supersymmetry and invariance under time‐reparametrization) can be relevant concerning the issue of supersymmetry breaking.     

Properties of the scalar potential in the supersymmetricSU(5) model

We investigate in detail the groundstates of the supersymmetricSU(5) model. The explicit breaking of supersymmetry is shown to be tightly restricted to select the phenomenologically desired vacuum. If the model contains two or more generations, a breaking of supersymmetry by a cosmological constant yields a potential which is not bounded from below.     

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.     

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.     

Dynamically broken supergravity and the hierarchy problem

We propose a scenario for grand unified models based on local supersymmetry. We give arguments that condensates of strongly interacting gauge theories might break local supersymmetry. The gravitino mass induces mass splittings in the low energy theory and allows us to understand a hierarchy of M_p = 10¹⁹ GeV to M_w = 10² GeV naturally.     

Conformal supersymmetry breaking and dynamical tuning of the cosmological constant

We propose “conformal supersymmetry breaking” models, which tightly relate the conformal breaking scale (i.e. R-symmetry breaking scale) and the supersymmetry breaking scale. Both the scales are originated from the constant term in the superpotential through the common source of the R-symmetry breaking. We show that dynamical tuning between those mass scales significantly reduces the degree of fine-tuning necessary for generating the almost vanishing cosmological constant.     

Effective lagrangian for supersymmetric theories with intermediate breaking scale

We investigate effective lagrangians in supersymmetric models broken spontaneously at an intermediate energy (～ μ ? M_GUT). It is shown to all orders in perturbation theory that the low-energy interactions of light particles are described by an effective lagrangian with explicit but soft supersymmetry breaking of order μ² / M_GUT.     

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.     

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.     

Symmetry Breaking for Matter Coupled to Linearized Supergravity from the Perspective of the Current Supermultiplet

We consider a generic supersymmetric matter theory coupled to linearized supergravity, and analyze scenarios for spontaneous symmetry breaking in terms of vacuum expectation values of components of the current supermultiplet. When the vacuum expectation of the energy momentum tensor is zero, but the scalar current or pseudoscalar current gets an expectation, evaluation of the gravitino self energy using the supersymmetry current algebra shows that there is an induced gravitino mass term. The structure of this term generalizes the supergravity action with cosmological constant to theories with CP violation. When the vacuum expectation of the energy momentum tensor is nonzero, supersymmetry is broken; requiring cancellation of the cosmological constant gives the corresponding generalized gravitino mass formula.     

Spacetime supersymmetry breaking in heterotic string theory

A simple mechanism for spacetime supersymmetry breaking in the ten-dimensional heterotic string theory is proposed. We present a heterotic string model with a hidden two-dimensional sigma-model sector which can induce desirably small supersymmetry breaking, without upsetting the zero value of the cosmological constant, through a topological instanton effect due to an abelian gauge field on the string world sheet. We find that the consistency condition of the gravitino field equation is satisfied for some configurations even after supersymmetry breaking.     

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.     

ΔB = 2 transitions in supersymmetric theories

We carry out a systematic analysis of ΔB = 2 interactions in supersymmetric theories. The selection rules in ΔB = 2 transition depend on the relative value of M (the mass scale that characterizes the ΔB = 2 interactions) and Λ_s (the super-symmetry-breaking scale). In particular, if M ? 10⁴GeV and Λ_s ～ 10²GeV, the effective ΔB = 2 interactions induce NN annihilation in a nucleus yielding two kaons in the final state while processes with only one or zero kaons are suppressed by mixing angles. On the other hand, if M ? 10⁴GeV, then supersymmetry does not imply any additional selection rules beyond those of ordinary (non-supersymmetric) theories.     

Minimal inflation

Using the universal X-superfield that measures in the UV the violation of conformal invariance we build up a model of multifield inflation. The underlying dynamics is the one controlling the natural flow of this field in the IR to the goldstino superfield once SUSY is broken. We show that flat directions satisfying the slow-roll conditions exist only if R-symmetry is broken. Naturalness of our model leads to scales of SUSY breaking of the order of 10^11–13 GeV, a nearly scale-invariant spectrum of the initial perturbations and negligible gravitational waves. We obtain that the inflaton field is lighter than the gravitino by an amount determined by the slow-roll parameter η. The existence of slow-roll conditions is directly linked to the values of supersymmetry and R-symmetry breaking scales. We make cosmological predictions of our model and compare them to current data.     

Catoptric tadpoles

Fermionic string perturbation theory is known to suffer from an ambiguity in the form of a total derivative in the moduli space. For a class of backgrounds (including R¹⁰, orbifolds and theories with no U(1) factors in gauge group) we show that these ambiguities for the partition function of heterotic string theory at any genus are proportional to massless physical tadpoles in the theory at lower genera and hence vanish in stable vacua. We also find that in R¹⁰ the cosmological constant at a given genus is proportional to the cosmological constant at lower genera. This enables us to give an inductive argument for the vanishing of the cosmological constant in R¹⁰ to all orders in string perturbation theory. We also address the ambiguity and finiteness of n-point functions. Our results indicate that in R¹⁰ the ambiguity can be absorbed by a renormalization of the string coupling constant and the string tension. The expected sources of divergence in the n-point function in arbitrary tachyon-free backgrounds, besides the usual infrared divergences for d ≤ 4, are shown to be proportional to tadpoles of physical massless fields. For type II strings in arbitrary backgrounds, we show by explicit calculations that the ambiguity vanishes at g = 2.     

Primordial inflation and present-day cosmological constant from extra dimensions

A semiclassical gravitation model is outlined which makes use of the Casimir energy density of vacuum fluctuations in extra compactified dimensions to produce the present-day cosmological constant as ρ _Λ ∼M ⁸/M _P ⁴, where M _P is the Planck scale and M is the weak interaction scale. The model is based on (4+D)-dimensional gravity, with D=2 extra dimensions with radius b(t) curled up at the ADD length scale b ₀=M _P /M ²∼0.1 mm. Vacuum fluctuations in the compactified space perturb b ₀ very slightly, generating a small present-day cosmological constant.The radius of the compactified dimensions is predicted to be b ₀≈k ^1/40.09 mm (or equivalently M≈2.4 TeV/k ^1/8), where the Casimir energy density is k/b ⁴.Primordial inflation of our three-dimensional space occurs as in the cosmology of the ADD model as the inflaton b(t), which initially is on the order of 1/M∼10⁻¹⁷ cm, rolls down its potential to b ₀.     

Electrovac universes with a cosmological constant

We present the extension of the Einstein-Maxwell system called electrovac universes by introducing a cosmological constant Λ. In the absence of the Λ term, the crucial equation in solving the Einstein-Maxwell system is the Laplace equation. The cosmological constant modifies this equation to become in a nonlinear partial differential equation which takes the form ΔU =2ΛU ³. We offer special solutions of this equation.     

Cosmological constant in SUGRA models and the multiple-point principle

Physics of Atomic Nuclei - An attempt is made to explain the tiny order of magnitude of the cosmological constant in a model involvingt he following ingredients: supersymmetry breaking in N = 1...