Spontaneous breaking of supersymmetry through dimensional reduction

A general technique for deriving consistent theories with spontaneously broken supersymmetry and massive gravitinos is illustrated by exploiting the chiral invariance of N = 1 supergravity in four dimensions to construct a theory with broken N = 2 supersymmetry in three dimensions.     

Supersymmetry and the Goldstino-like mode in bose-fermi mixtures

Supersymmetry is assumed to be a basic symmetry of the world in many high-energy theories, but none of the superpartners of any known elementary particle have been observed yet. We argue that supersymmetry can also be realized and studied in ultracold atomic systems with a mixture of bosons and fermions, with properly tuned interactions and single particle dispersion. We further show that in such nonrelativistic systems supersymmetry is either spontaneously broken or explicitly broken by a chemical potential difference between the bosons and fermions. In both cases the system supports a sharp fermionic collective mode similar to the Goldstino mode in high-energy physics, due to supersymmetry. We also discuss possible ways to detect this mode experimentally.     

Spontaneous supersymmetry breaking by large-N matrices

Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity. In our models, the large value of N gives a natural explanation for the origin of small parameters appearing in the field theories which trigger the supersymmetry breaking.     

Essay: Supersymmetry, the Cosmological Constant, and a Theory of Quantum Gravity in Our Universe

There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterizes different theories. If it is positive, supersymmetry must be broken. A heuristic calculation shows that a cosmological constant of the observed size predicts superpartners in the TeV range. This mechanism for SUSY breaking also puts important constraints on low energy particle physics models.     

Solution of the gauge hierarchy problem

We propose a novel solution to the gauge hierarchy problem in theories with softly broken supersymmetry. Quantum effects can resuscitate classically sick theories, producing the large scale from the small supersymmetry breaking scale. We use this mechanism to construct realistic SU(6) and SU(5) GUTs which do not suffer from gauge hierarchy or fine tuning problems.     

Spontaneous breakdown and finiteness of supersymmetric theories in two dimensions

Using a single scalar superfield we construct the two dimensional version of the four dimensional Wess-Zumino model and examine its renormalization properties. In the context of this model and in the tree approximation we find that supersymmetry can be spontaneously broken with the appearance of a massless fermion. This solution is then shown to be dynamically unstable at the one-loop level. Finally we use supersymmetry to construct two dimensional theories for which all IPI vertices are finite.     

Temperature and supersymmetry

We study equal-time correlation functions at finite temperature in field theories with global supersymmetry. Global supersymmetry is found to be broken at finite temperature; the ground state is not supersymmetric but no Goldstone fermion appears. The temperature dependence of the mass spectrum in the one-loop approximation and leading order in temperature is investigated in several models. In the models that we consider with spontaneous supersymmetry breaking we find that the Goldstone fermion remains massless at the one-loop level. Ward identities describing the supersymmetry of the underlying theory are checked at the one-loop level. We also discuss the situation in supergravity.     

Anomaly,gauge and gaugino mediation in brane worlds with messenger matter

Theories in which supersymmetry is broken on another brane, which is separated from the minimal supersymmetry standard model (MSSM) matter fields in an extra dimension, are attractive because they may solve the supersymmetric flavor problem. We consider the effects in such theories of new messenger fields with standard model gauge charges and with direct couplings to the supersymmetry breaking sector. The effect on the masses of the MSSM superpartners can be dramatic. In particular, the tachyonic slepton problem of anomaly mediation and the stable slepton problem of gaugino mediation can be cured.     

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.     

Anomaly constraints on supersymmetric effective lagrangians

In this paper we set constraints on the possible effective-lagrangian representations of supersymmetric gauge theories with spontaneously broken chiral flavor symmetries, by finding the conditions under which a Wess-Zumino term to represent the anomalous interactions can be constructed. We find that effective lagrangians for such theories are possible only for nonlinear sigma models defined on noncompact manifolds, and demonstrate the realization of this result in supersymmetric QCD. We also consider the Wess-Zumino term in the nonlinear realization of broken supersymmetry.     

Dynamical supersymmetry breaking in two-dimensional N = 1 supergravity theories

We investigate a possible dynamical mechanism for spontaneous supersymmetrybreaking in N = 1 supergravity theories in 1 + 1 space-time dimensions. It will be shown that supersymmetry is never broken at the tree level, but it can be broken for a certain class of models by quantum effects due to trace anomalies of the energy-momentum tensor and the supercurrent.     

See-saw and supersymmetry or exact R-parity

We show how the renormalizable see-saw mechanism in the context of supersymmetry and spontaneously broken B−L symmetry implies exact R-parity at all energies. We argue that supersymmetry plays an important role in providing a “canonical” form for the see-saw, in particular in grand unified theories that solve the doublet-triplet splitting problem via the Dimopoulos–Wilczek mechanism.     

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.     

Towards Higher-N Superextensions of Born–Infeld Theory

We give a brief account of supersymmetric Born–Infeld theories with extended supersymmetry, including those with partially broken supersymmetry. Some latest developments in this area are presented. One of them is N = 3 supersymmetric Born–Infeld theory which admits a natural off-shell formulation in N = 3 harmonic superspace.     

Supersymmetric field theories at finite temperature

We show by explicit calculations to second and third order in perturbation theory, that finite temperature effects do not break the supersymmetry Ward-Takahashi identities for graded thermal Green functions of the Wess-Zumino model. Moreover, it is argued that this result is true to all orders in perturbation theory, and further, true for a wide class of supersymmetric theories. We point out, however, that these identities can be broken in the course of a phase transition that restores an originally broken internal symmetry.     

The supersymmetric Higgs mechanism—Quartet decoupling and nondoubled Goldstone bosons

A complete quantum field theoretic analysis of the supersymmetric Higgs mechanism is presented, in the general case where the Goldstone bosons may be either doubled or nondoubled. If gauge fields are coupled to nondoubled Goldstone bosons, it is found that supersymmetry is spontaneously broken not just by the masses but also by the spins of the physical particles. The spectrum reveals no supersymmetry multiplet structure. The decoupling of unphysical degrees of freedom is carefully discussed, and the quartet decoupling mechanism for gauged Goldstone bosons is extended to supersymmetry theories. The results are illustrated with an SU(2) × U(1) model.     

Supersymmetric sound in condensed matter

The effect of a net conserved charge density is considered in supersymmetric relativistic field theories. If the charge is supersymmetric and if it distributes itself homogeneously, there appear both goldstino and Goldstone modes, associated with the spontaneously broken supersymmetry algebra.     

Supersymmetric preon models with gauged colour-flavour symmetry

We have conducted a search for globally supersymmetric preon models with gauged colour-flavour symmetries. Theories with both two- and three-preon composites, and colour-flavour groups from E₆ down to the standard model, are examined under the following conditions: asymptotically-free metacolour, anomaly-free gauged symmetries, and Pauli principle obeyed. It is found that there are no models with three or more supersymmetric families. If supersymmetry is broken, one model with four families emerges. The purely fermionic preon theories can also be considered as the light sector of a chiral supersymmetric theory, with supersymmetry breaking at the preon level.     

The many-body content of quantum gauge theories and spontaneous symmetry breaking

The many-body content of quantum field theories is studied by performing the limit velocity of light → ∞. It is found that the limit of the Goldstone model is the Bogoliubov model of superfluidity, and the limit of the vacuum of spontaneously broken abelian theories is a plasma whose excitations are the limit of the massive gauge bosons. The method appears suitable to study dynamical supersymmetry breaking and colour confinement.     

Nonlinear supersymmetry without the GSO projection and unstable D9-brane

Orientable open string theories containing both bosons and fermions without the GSO projection are expected to have the 10-dimensional N=2 space–time supersymmetry in a spontaneously broken phase. We study the low-energy theorem for the nonlinearly realized N=2 supersymmetry using the effective action for an unstable D9-brane. It is explicitly confirmed that the 4-fermion open string amplitudes without the GSO projection obey the low-energy theorem derived from the nonlinear N=2 supersymmetry. An intimate connection between the existence of the hidden supersymmetry and the open–open string (s–t) duality is pointed out.