Finiteness, 1/N expansion and supersymmetry breaking

The possibility of spontaneous supersymmetry breaking in the limit of large N, in models with an internal O(N) symmetry, is demonstrated by constructing an explicit example in two dimensions. The model is finite and this is shown to be important for the supersymmetry breaking. A general criterion for finiteness of scalar superfield theories in two dimensions is given. Finally, the generalization of our results to three dimensions, and their relevance to four-dimensional models, is discussed.     

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.     

Supersymmetric mini-superspace

A mini-superspace model for quantum cosmology which possesses local supersymmetry is found by reducing N = 1 supergravity in a k = + 1 Friedmann model, and its classical and quantum solutions are discussed. In a more general class of supersymmetric models containing a scalar field, it may still be possible to compute the Hartle-Hawking state.     

N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory

Boundary integrable models with N=2 supersymmetry are considered. For the simplest boundary N=2 superconformal minimal model with a Chebyshev bulk perturbation we show explicitly how fermionic boundary degrees of freedom arise naturally in the boundary perturbation in order to maintain integrability and N=2 supersymmetry. A new boundary reflection matrix is obtained for this model and N=2 boundary superalgebra is studied. A factorized scattering theory is proposed for a N=2 supersymmetric extension of the boundary sine-Gordon model with either (i) fermionic or (ii) bosonic and fermionic boundary degrees of freedom. Exact results are obtained for some quantum impurity problems: the boundary scaling Lee–Yang model, a massive deformation of the anisotropic Kondo model at the filling values g=2/(2n+3) and the boundary Ashkin–Teller model.     

Higgs masses in the standard,multi-Higgs and supersymmetric models

Theoretical constraints and limits on the masses of Higgs scalars in the standard electroweak model, in electroweak models with additional Higgs doublets and in various supersymmetric models are presented. In the standard model, the lower limit on the Higgs mass, based on vacuum stability arguments, is reviewed in detail, as are “upper limits” based on perturbative constraints. In most grand unified and all supersymmetric models, however, at least two doublets are needed. The masses of the various Higgs scalars in the two-doublet model are discussed and constraints on their masses are found, including the generalization of the above limits. The results are then generalized to models with more than two doublets. Finally, recent attempts at constructing models with low-energy supersymmetry are reviewed and it is shown that in many models, fairly stringent tree-level mass relations among the Higgs scalars can be found. These relations are interesting in that they do not refer to the supersymmetric partners of ordinary particles, and they are most restrictive in models in which the supersymmetry is explicitly broken, i.e., via arbitrary mass terms.     

Model building on asymmetric Z3 orbifolds: Non-supersymmetric models

Four-dimensional string models arising in the asymmetric Z₃ orbifold compactifications of the heterotic string are studied. A mechanism for supersymmetry breaking that gives rise to chiral models in four dimensions is presented, and some typical models are discussed. A formalism for calculating one-loop partition functions in Z₃ models is developed. One partition function is constructed that may correspond to a non-supersymmetric, tachyon-free theory, with a vanishing cosmological constant as a consequence of Atkin-Lehner symmetry. The negative result of a search for the model corresponding to this partition function is reported.     

The spinning superparticle

Doubly graded massless supersymmetric particle models with both world-line local and space-time global supersymmetry are considered. We describe the first quantization of the model with four-dimensional space-time and N=1 world-line SUSY. Using the Gupta-Bleuler method we obtain as the super wave-function a pair of D=4 chiral spinor superfields with the on-shell spectrum containing scalar and vector multiplets.     

Superconformal anomalies and the effective lagrangian for pure supersymmetric QCD

We discuss the extent to which the superconformal anomalies constrain the effective lagrangian for pure N = 1 Yang-Mills theory. Assuming that the order parameter describing the model is a single chiral superfield (and allowing its derivatives) we find a larger class of possible models than had been previously noted. We give a detailed analysis of a particularly interesting example and find that it leads to the possibility of spontaneous breakdown of supersymmetry. Thus we conclude that the anomaly constraints by themselves are not sufficient to protect supersymmetry. Some unusual features which seem characteristic of such higher derivative theories are noted. A number of related topics, including the question of gluon condensation, are discussed.     

Orbifold models and modular transformation

The orbifold models of the heterotic string are constructed on the quotient spaces of generalized tori by translational and rotational discrete symmetries. In order to obtain the consistent orbifold models, the conditions of the modular invariance are derived from a one-loop vacuum amplitude. Z₃ orbifold models satisfying such conditions are searched systematically. It is shown that there are infinite possible models with N = 2 supersymmetry. Among these models, two examples having E₆ and E₇ gauge groups are discussed. The orbifold models with N = 1 supersymmetry are also discussed in detail. It is shown that there are only five consistent models in the class of these models based on E₈ ⊗ E′₈ heterotic string in which the extra six-dimensional torus and the E₈ ⊗ E′₈ maximal torus are modded out by the rotational and the translational Z₃ symmetries respectively.     

Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.     

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.     

Supersymmetric models of weak and electromagnetic interactions

General method of spontaneous supersymmetry breaking is developed. On its basis a number of unified lepton models is analyzed. Examples of realistic lepton models based on the groups SU(2) × U(1) and SU(2) × SU(2) × U(1) are considered.     

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.     

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.     

Canonical supergravity potentials

We investigate the potentials of supergravity models with canonical kinetic energy and derive several properties. If the model isR-invariant with non-negativeR-charges, we prove that the potential is strictly positive and vanishes without finetuning if and only if supersymmetry is unbroken. Allowing for negativeR-charges we present a model where supersymmetry is broken in the absolute minimum which is finetuned toV _min=0.     

The sliding singlet

Supersymmetric grand unified models with a sliding singlet are considered. We review the argument that the sliding does not work in models with large supersymmetry breaking. Then we consider the possibility of using a sliding singlet with low-energy supersymmetry breaking. A number of problems with such a program are noted and illustrated in simple examples. Using the experience gained from these examples a realistic model is constructed and analyzed.     

Remarks on (0,2) models and intermediate scale scenarios in string theory

Problems associated with large intermediate scales in string theory are discussed. It is shown that, in σ-model perturbation theory, the superpotential of theories with (2,2) supersymmetry is purely cubic. As a result, to exhibit flat directions with (0,2) supersymmetry, one needs to study only a small number of Yukawa couplings. Usually these flat directions are lifted by nonperturbative effects in the σ model. Examples where this is not the case, due to Cvetic and to Distler and Greene, are discussed. It is shown that in the former case, there are not, generically, extra massless particles to play the role of Higgs fields. The problems of proton decay, neutrino masses, and obtaining light Higgs fields in models with large intermediate scales are considered, and various difficulties with existing proposals are pointed out.     

Softly broken supersymmetry and the fine-tuning problem

The supersymmetry of the simple Wess-Zumino model is broken, in the tree-approximation, by adding all possible parity-even [mass]-dimension 2 and 3 terms. The model is then renormalized using BPHZ and the normal product algorithm, such that supersymmetry is only softly broken (in the original sense of Schroer and Symanzik).We show that, within the above renormalization scheme, none of the added breaking terms give rise to technical fine-tuning problems (defined in the sense of Gildener) in larger models, with scalar multiplets and hierarchy of mass scales, which is in contrast to what we obtain via analytic schemes such as dimensional renormalization, or supersymmetry extension of which.The discrepancy (which can be shown to persist in more general models) originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Emphasizing that the issue is purely technical (as opposed to physical) in origin, and that all physical properties are scheme-independent (as they should be!), we conclude that the technical fine-tuning problem, in the specific sense used in this paper, being scheme dependent, is not a well-defined issue within the context of renormalized perturbation theory.     

The muon magnetic moment and new physics

The impact of the muon magnetic moment measurement on physics beyond the Standard Model is briefly reviewed. Particular emphasis is given on the case of supersymmetry. The sensitivity of g ? 2 to supersymmetry parameters and the potential for model discrimination and parameter measurements is described. The interplay between LHC data on the Higgs boson, limits on new particles, and g ? 2 is discussed.