Comment on the supersymmetry at finite temperatures

We comment on some of the general thermostatistical properties of the global supersymmetry characterized by Grassmann parameters, which are shared by the ordinary supersymmetry as well as by the BRS supersymmetry associated with any gauge symmetry including local supersymmetry.     

Dynamical stability of the BRS supersymmetry and the Gribov problem

The stability of the Becchi-Rouet-Stora supersymmetry is studied on the basis of a simple non-gauge model invariant under BRS supersymmetry. The Nambu-Goldstone theorem is stated and the spontaneous breakdown of the BRS supersymmetry is illustrated by the above non-gauge model. This indicates that the dynamical stability of BRS supersymmetry in non-abelian gauge theories should also be carefully examined, if one takes the Faddeev-Popov lagrangian as a basis of the formal canonical treatment. We show that a better understanding of the Gribov problem is required to establish the stability of the BRS supersymmetry in non-abelian gauge theories to non-perturbative accuracy.     

Dynamical breaking of supersymmetry

General conditions for dynamical supersymmetry breaking are discussed. Very small effects that would usually be ignored, such as instantons of a grand unified theory, might break supersymmetry at a low energy scale. Examples are given (in 0 + 1 and 2 + 1 dimensions) in which dynamical supersymmetry breaking occurs. Difficulties that confront such a program in four dimensions are described.     

Transformation properties of the supercurrent

It is shown that the spinor current, if correctly defined, belongs to a supermultiplet, together with the energy-momentum tensor and the axial-vector current. The transformation properties of this supermultiplet under both restricted and general supersymmetry transformations are given. The generators of special supersymmetry transformations can be obtained as first moments of the time component of the spinor current. The transformation laws of the supermultiplet containing the spinor current provide the local version of the supersymmetry algebra.     

Dirac neutrino masses from generalized supersymmetry breaking

We demonstrate that Dirac neutrino masses in the experimentally preferred range are generated within supersymmetric gauge extensions of the standard model with a generalized supersymmetry breaking sector. If the superpotential neutrino Yukawa terms are forbidden by the gauge symmetry [such as a U(1)'], sub-eV scale effective Dirac mass terms can arise at tree level from hard supersymmetry breaking Yukawa couplings, or at one loop due to nonanalytic soft supersymmetry breaking trilinear scalar couplings. The radiative neutrino magnetic and electric dipole moments vanish at one-loop order.     

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.     

Supersymmetry in superspace: 35 years of the research activity in LTP

This is an overview of the all-years research activity in supersymmetry in the Markov-Ogievetsky group at the Bogoliubov Laboratory of Theoretical Physics. It started shortly after the discovery of supersymmetry and is lasting for more than 30 years. In this survey the main emphasis is made on the superspace geometric approaches and unconstrained superfield formulations. Alongside such milestones as the geometric formulation of supergravity and the harmonic superspace approach to extended supersymmetry, some other developments largely contributed by the Dubna theorists are briefly accounted for. The text was submitted by the author in English.     

Supersymmetry and positive temperature for simple systems

It has recently been argued by Girardello et al. that supersymmetry is automatically broken at positive temperature even when unbroken at T = 0, in the sense that the usual derivation of identities from unbroken supersymmetry does not automatically generalize to T > 0. Using as a guide simple examples with one bosonic and one fermionic degree of freedom, we study how supersymmetry reflects itself in the properties of excited states, in particular in the thermal properties at positive temperature. We derive a class of relations [see eq. 1.2)] which extend to all T the familiar consequences of unbroken supersymmetry for ground-state expectation values; these relations hold for unbroken and spontaneously broken supersymmetry. With Levine and Tomozawa we consider the algebra generated by the supercharges. In the case of two supercharges it can be reduced to the Clifford algebra of Pauli spin matrices, for which the eigenstates form irreducible doublets, except that a zero-energy eigenstate may be a singlet. The relations mentioned above are shown to hold for each doublet individually [see eq. (4,7)]. Some additional remarks are made on supersymmetry breaking at zero and positive temperatures.     

Toward a unification of “everything” with gravity

Combining the ideas of gauge interactions with a global supersymmetry, we build a unified model in six dimensions step by step, starting with a single generation of leptons and ending with three generations of leptons and colored quarks forming a supermultiplet characterized by a most general extensionN=8. The puzzle of supersymmetric partners, such as the gravitino, photino, s-leptons, and s-quarks, is seen in a new light. The supersymmetry is only a global one, whereas local supersymmetry and supergravity are replaced by the theory of gauge interactions and by the usual general relativity of Einstein.     

Supersymmetry transformation of quantum fields

If supersymmetry is realized non-linearly as is the case when auxiliary fields are eliminated and/or one works in the Wess–Zumino gauge it is usually incorporated in terms of BRS transformations and Slavnov–Taylor identities. On the vertex functional susy transformations act even non-locally. Furthermore, the gauge fixing term breaks supersymmetry. In the present paper we clarify in which sense supersymmetry is still a symmetry of the system and how it is realized on the level of quantum fields. We treat the Wess–Zumino model as an example for chiral models, SQED and massless SYM as prototypes of gauge theories.     

Non‐linear Realizations and Higher Curvature Supergravity

We focus on non‐linear realizations of local supersymmetry as obtained by using constrained superfields in supergravity. New constraints, beyond those of rigid supersymmetry, are obtained whenever curvature multiplets are affected as well as higher derivative interactions are introduced. In particular, a new constraint, which removes a very massive gravitino is introduced, and in the rigid limit it merely reduces to an explicit supersymmetry breaking. Higher curvature supergravities free of ghosts and instabilities are also obtained in this way. Finally, we consider direct coupling of the goldstino multiplet to the super Gauss–Bonnet multiplet and discuss the emergence of a new scalar degree of freedom.     

Supergravity as a gauge theory of supersymmetry

In a new approach to supergravity we consider the gauge theory of the 14-dimensional supersymmetry group. The theory is constructed from 14×4 gauge fields, 4 gauge fields being associated with each of the 14 generators of supersymmetry. The gauge fields corresponding to the 10 generators of the Poincaré subgroup are those normally associated with general relativity, and the gauge fields corresponding to the 4 generators of supersymmetry transformations are identified with a Rarita-Schwinger spinor. The transformation laws of the gauge fields and the Lagrangian of lowest degree are uniquely constructed from the supersymmetry algebra. The resulting action is shown to be invariant under these gauge transformations if the translation associated field strength vanishes. It is shown that the second-order form of the action, which is the same as that previously proposed, is invariant without constraint.     

Finite-temperature supersymmetry: the Wess-Zumino model

We investigate the breakdown of supersymmetry at finite temperature. While it has been proven that temperature always breaks supersymmetry, the nature of this breaking is less clear. On the one hand, a study of the Ward-Takahashi identities suggests a spontaneous breakdown of supersymmetry without the existence of a Goldstino, while on the other hand it has been shown that in any supersymmetric plasma there should exist a massless fermionic collective excitation, the phonino. Aim of this work is to unify these two approaches. For the Wess-Zumino model, it is shown that the phonino exists and contributes to the supersymmetric Ward-Takahashi identities in the right way displaying that supersymmetry is broken spontaneously with the phonino as the Goldstone fermion.     

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.     

Supersymmetry and LHC

Motivations for introducing supersymmetry in high-energy physics are discussed along with the possibility of discovering supersymmetry at the Large Hadron Collider (LHC). Various regions of the space of parameters of the minimal supersymmetric standard model are analyzed, and phenomenological manifestations of supersymmetry inherent in these regions are discussed. The discovery potential of LHC at the planned luminosity is indicated for various channels.     

Supersymmetrical string theories

A supersymmetrical light-cone-gauge string action is presented. It provides a basis for understanding the previously- studied supersymmetrical dual string theory as well as two new closed-string theories that have extended supersymmetry in ten dimensions, corresponding to N=8 supersymmetry in four dimensions.     

A supersymmetric gut

We propose a grand unified supersymmetric theory based on SU(5) with spontaneously broken supersymmetry. The theory (really a class of theories) is completely realistic. In particular, supersymmetry partners of ordinary fermions and bosons are heavy. The model requires one fine-tuning in order to render the color triplet partners of the Higgs fields (which mediate proton decay) superheavy. This fine-tuning is stable against radiative corrections. At the tree level, the model contains two scales, the unification scale, of order 10¹⁶ GeV, and the supersymmetry breaking scale, of order 10¹⁰ GeV. The breaking of SU(2) × U(1) invariance arises as a radiative effect. The lightest of the new particles implied by supersymmetry are expected to have masses of order tens of GeV.     

Supersymmetrical dual string theory

It is proved that the physical states of the open-string sector of the ten-dimensional string theory form supersymmetry multiplets. The proof is achieved by first constructing a new formulation of the spectrum generating algebra, and then forming the supersymmetry operator (as well as associated operators) and demonstrating that it transforms as a spinor under Lorentz transformations and has the correct anticommutation relations. The results can be interpreted either in terms of a covariant formulation or in terms of a light-cone gauge formulation. In the former case certain formulas are not completely proved, although they are in the latter. When interpreted in four dimensions (by dimensional reduction) the string theory provides an interacting theory of an infinite number of massive representations of N = 4 supersymmetry involving particles of arbitrarily high spin.     

Primordial cosmological inflation versus local supersymmetry breaking in SUSY GUTs coupled toN=1 supergravity

We present a model for a SUSY GUT coupled toN=1 supergravity in which local supersymmetry breaks down in the gauge singlet sector. The constraints for the model to be physically acceptable are incompatible with inflation. The simultaneous breaking of local supersymmetry and gauge symmetry is proposed as a good prospect for inflation.