ON THE DYNAMICAL SYMMETRY BREAKING FOR THE N=l PURE SUPERSYMMETRIC YANG-MILLS MODEL

An approximate effective Lagrangian of composite operators in superfield formalism for the N=l pure supersymmetric Yang-Mills model is obtained with the help of renormalization group equations for the generating functional. While the supersymmetry is always kept unbroken by this effective Lagrangian we find that the chiral symmetry may and may not be unbroken.     

A quantum Hamilton–Jacobi proof of the nodal structure of the wave functions of supersymmetric partner potentials

Quantum Hamilton–Jacobi formalism is used to give a proof for Gozzi’s criterion, which states that for eigenstates of the supersymmetric partners, corresponding to the same energy, the difference in the number of nodes is equal to one when supersymmetry (SUSY) is unbroken and is zero when SUSY is broken. We also show that this proof is also applicable to the case, where isospectral deformation is involved.     

Patterns of symmetry breaking in supersymmetric gauge theories

We give a group-theoretical analysis of the spontaneous breaking of the gauge group in supersymmetric Yang-Mills theories with unbroken supersymmetry.     

The soliton supermultiplet in 4 + 1 dimensions

We consider the SO(4) = SU(2) ? USp(2) Clifford algebra, obtained by the supersymmetry algebra for the N = 2 supersymmetric Yang-Mills theory in 4+1 dimensions, which, in the phase of unbroken gauge symmetry, has a topological charge as central charge. We find that, even if the Higgs mechanism is absent, the massive soliton supermultiplet contains the same number of states as the massless supermultiplet of elementary particles.     

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.     

On the supersymmetric solitons and monopoles

The basic results in a new trend in supersymmetry and soliton theory are presented. It is shown that the soliton expectation value of the energy operator is the mass of the soliton without quantum corrections. A new supersymmetric monopole model in three dimensions is constructed by generalization of the supersymmetric sine-Gordon model in one space dimension.     

Aspects of supersymmetric quantum mechanics

We review the properties of supersymmetric quantum mechanics for a class of models proposed by Witten. Using both Hamiltonian and path integral formulations, we give general conditions for which supersymmetry is broken (unbroken) by quantum fluctuations. The spectrum of states is discussed, and a virial theorem is derived for the energy. We also show that the euclidean path integral for supersymmetric quantum mechanics is equivalent to a classical stochastic process when the supersymmetry is unbroken (E₀ = 0). By solving a Fokker-Planck equation for the classical probability distribution, we find P_c(y) is identical to |Ψ₀(y)|² in the quantum theory.     

Supersymmetry anomally in two dimensions

In two dimensions we obtain a supersymmetric extension of a gauge anomaly, and find that this is the origin of a supersymmetry anomaly in the Wess-Zumino gauge. We also obtain an effective action whose variations give rise to the gauge and supersymmetry anomalies.     

A GENERATION OF EXACTLY SOLVABLE ANHARMONIC SYMMETRIC OSCILLATORS

Using the ideas of supersymmetric quantum mechanics, we exactly solve a continuous family of anharmonic potentials, which are the supersymmetric partners of the linear harmonic oscillators. The family includes a series of potentials in which the excited-state energy is the same as that of the harmonic oscillators, but the ground-state energy can be any value lower than the excited states. The shape of the potential is variable, which includes the double-well and triple-well potentials. All the potentials obtained in this paper are free of singularities, and the supersymmetry of the solutions is unbroken.     

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.     

A Comment on the Light-Cone Vacuum in 1+1 Dimensional Super-Yang–Mills Theory

The discrete light-cone quantization (DLCQ) of a supersymmetric gauge theory in 1+1 dimensions is discussed, with particular attention given to the inclusion of the gauge zero mode. Interestingly, the notorious zero-mode problem is now tractable because of special supersymmetric cancellations. In particular, we show that anomalous zero-mode contributions to the currents are absent, in contrast to what is observed in the nonsupersymmetric case. An analysis of the vacuum structure is provided by deriving the effective quantum mechanical Hamiltonian of the gauge zero mode. It is shown that the inclusion of the zero modes of the adjoint scalars and fermions is crucial for probing the phase properties of the vacua. We find that the ground-state energy is zero and thus consistent with unbroken supersymmetry and conclude that the light-cone Fock vacuum is unchanged with or without the presence of matter fields.     

Nonlinear supersymmetry,quantum anomaly and quasi-exactly solvable systems

The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to a supersymmetric canonical system with the holomorphic form of the supercharges. Depending on the behaviour of the superpotential, the canonical supersymmetric systems are separated into the three classes. In one of them the parameter specifying the supersymmetry order is subject to some sort of classical quantization, whereas the supersymmetry of another extreme class has a rather fictive nature since its fermion degrees of freedom are decoupled completely by a canonical transformation. The nonlinear supersymmetry with polynomial in momentum supercharges is analysed, and the most general one-parametric Calogero-like solution with the second order supercharges is found. Quantization of the systems of the canonical form reveals the two anomaly-free classes, one of which gives rise naturally to the quasi-exactly solvable systems. The quantum anomaly problem for the Calogero-like models is “cured” by the specific superpotential-dependent term of order ℏ². The nonlinear supersymmetry admits the generalization to the case of two-dimensional systems.     

Supersymmetry in Lorentzian Curved Spaces and Holography

We consider superconformal and supersymmetric field theories on four-dimensional Lorentzian curved space-times, and their five-dimensional holographic duals. As in the Euclidean signature case, preserved supersymmetry for a superconformal theory is equivalent to the existence of a charged conformal Killing spinor. Differently from the Euclidean case, we show that the existence of such spinors is equivalent to the existence of a null conformal Killing vector. For a supersymmetric field theory with an R-symmetry, this vector field is further restricted to be Killing. We demonstrate how these results agree with the existing classification of supersymmetric solutions of minimal gauged supergravity in five dimensions.     

Local supersymmetry anomaly in two dimensions

We study the local supersymmetry anomaly by constructing an N = 1 (counted by Majorana-Weyl spinors) chiral supergravity model in two dimensions. There is the local supersymmetry anomaly as well as the gravitational anomaly. We obtain the linearized forms of these anomalies by perturbation calculation. The full non-linear forms are obtained by finding a solution to the Wess-Zumino consistency condition. These anomalies can be derived from the supersymmetric extension of the Chern-Simons invariant in three dimensions.     

Dynamics of compositeW-bosons

We derive some constraints among the masses and couplings of theW-bosons and the vacuum condensates of some non-supersymmetric and supersymmetric theories where theW are composite particles. We deduce that in a theory where the value of the hypergluon condensate is much smaller than the value of the compositeness scale (like in the case of an unbroken supersymmetry), theW-bosons cannot be composite.     

The (2+1)-dimensional supersymmetric CPN−1 model and the central charge

The supersymmetry algebra is examined for the (2+1)-dimensional supersymmetric CP^N?1 model, on the basis of the observation of Witten and Olive in (1+1) and (3+1) dimensions. We then demonstrate that also in this (2+1)-dimensional model the usual supersymmetry algebra is modified by the appearance of the topological numbers of the solitons, which are nothing but the instantons in (1+1) dimensions, as central charges. To obtain the model, we begin by constructing the supersymmetric model in (3+1) dimensions. Then it is reduced to (2+1) dimensions by means of the dimensional reduction technique. We observe that the (2+1)-dimensional supersymmetric CP^N?1 model thus obtained admits an O(2) extended supersymmetry.     

Dynamical supersymmetry breaking in a finite field theoretical model

We present a supersymmetric field theory in two or three space-time dimensions with an internal symmetry of the O(N) type. In the large-N limit the model is finite and supersymmetry is spontaneously broken. The fields representing the order parameters of the broken supersymmetry phase acquire dynamics through quantum corrections. In particular the Goldstone fermion is a zero-mass fermionic bound state.     

Non-supersymmetric orientifolds of Gepner models

Starting from a previously collected set of tachyon-free closed strings, we search for N=2$N=2$ minimal model orientifold spectra which contain the standard model and are free of tachyons and tadpoles at lowest order. For each class of tachyon-free closed strings – bulk supersymmetry, automorphism invariants or Klein bottle projection – we do indeed find non-supersymmetric and tachyon free chiral brane configurations that contain the standard model. However, a tadpole-cancelling hidden sector could only be found in the case of bulk supersymmetry. Although about half of the examples we have found make use of branes that break the bulk space–time supersymmetry, the resulting massless open string spectra are nevertheless supersymmetric in all cases. Dropping the requirement that the standard model be contained in the spectrum, we find chiral tachyon and tadpole-free solutions in all three cases, although in the case of bulk supersymmetry all massless spectra are supersymmetric. In the other two cases we find truly non-supersymmetric spectra, but a large fraction of them are nevertheless partly or fully supersymmetric at the massless level.     

Supersymmetry among free fermions and superstrings

A complete classification is given of all supersymmetric theories of free massless two-dimensional fermions. This, in particular, implies a classification of all free-fermion representations of super Kac-Moody algebras. It is shown that these cannot be used to construct new string theories with unbroken supersymmetry in Minkowski space-time, other than the torus-compactifications of the known ten-dimensional superstrings. Assuming anti-de-Sitter space-time could restore conformal invariance, it is shown how one could construct a string theory whose low-lying excitations form a multiplet of gauged N = 8 supergravity.     

Index theorems and supersymmetry in the soliton sector

For arbitrary two-dimensional supersymmetric theories with soliton solutions, we use the Callias-Bott-Seeley trace theorem to calculate the O(?) correction to the soliton mass. At the same order the Bogomolny bound is shown, by an explicit computation, to be saturated. The non-vanishing of the mass correction is traced to the existence of supersymmetry violating surface terms in the soliton lagrangian, while the saturation of the Bogomolny bound is a consequence of the absence of spontaneous breaking of $\text{N =}\text{1}\text{2}$ supersymmetry in a related lagrangian. We argue that this supersymmetry remains unbroken to all orders in perturbation theory. Topological arguments à la Witten are not able to exclude non-perturbative breaking.