Positive energy without supersymmetry

Witten's positive energy theorem and its generalizations can be viewed as stating that supersymmetric solutions of any supergravity theory are stable. In this paper we give a criterion to test the stability of non-supersymmetric solutions of supergravity theories and solutions of theories which cannot be embedded in a supergravity theory. Previously some of these solutions might have been considered to be unstable. In particular, we show that the non-supersymmetric stationary point of the scalar potential of the gauged N = 5 supergravity theory is stable. We also give an elegant derivation of the Breitenlohner-Freedman condition for (small fluctuation) stability.     

Metastable supersymmetry breaking without scales

We construct new examples of models of metastable D=4$D=4$N=1$N=1$ supersymmetry breaking in which all scales are generated dynamically. Our models rely on Seiberg duality and on the ISS mechanism of supersymmetry breaking in massive SQCD. Some of the electric quark superfields arise as composites of a strongly coupled gauge sector. This allows us to start with a simple cubic superpotential and an asymptotically free gauge group in the ultraviolet, and end up with an infrared effective theory which breaks supersymmetry dynamically in a metastable state.     

Weak scale supersymmetry without weak scale supergravity

It is generally believed that weak scale supersymmetry implies weak scale supergravity, in the sense that the masses of the gravitino and gravitationally coupled moduli have masses below 100 TeV. This Letter presents a realistic framework for supersymmetry breaking in which these masses can be much larger. This solves the cosmological problems of hidden sector models. Supersymmetry breaking is communicated to the visible sector by anomaly-mediated supersymmetry breaking. The framework is compatible with perturbative gauge coupling unification and can be realized either in models of "warped" extra dimensions or in strongly coupled four-dimensional conformal field theories.     

Nonlinear supersymmetry on the plane in magnetic field and quasi-exactly solvable systems

The nonlinear n-supersymmetry with holomorphic supercharges is investigated for the 2D system describing the motion of a charged spin-1/2 particle in an external magnetic field. The universal algebraic structure underlying the holomorphic n-supersymmetry is found. It is shown that the essential difference of the 2D realization of the holomorphic n-supersymmetry from the 1D case recently analysed by us consists in appearance of the central charge entering non-trivially into the superalgebra. The relation of the 2D holomorphic n-supersymmetry to the 1D quasi-exactly solvable (QES) problems is demonstrated by means of the reduction of the systems with hyperbolic or trigonometric form of the magnetic field. The reduction of the n-supersymmetric system with the polynomial magnetic field results in the family of the one-dimensional QES systems with the sextic potential. Unlike the original 2D holomorphic supersymmetry, the reduced 1D supersymmetry associated with x⁶+⋯ family is characterized by the non-holomorphic supercharges of the special form found by Aoyama et al.     

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.     

Finite field theories in three dimensions with and without supersymmetry

Necessary and sufficient conditions are derived for the finiteness of theS-matrix and vacuum stress of theories with Yukawa,? ³, and? ⁴ couplings in three spacetime dimensions, and general supersymmetric solutions to these conditions are given. The requirement of a finiteS-matrix allows many non-supersymmetric solutions, but with two bosons and two fermions the additional constraint of a finite vacuum stress allows only one simple alternative to supersymmetry.     

Dynamical properties of the vacuum in non-abelian field theories with and without supersymmetry

In QCD with massless quarks, the effective potential for the color singlet operator (F_μν^a)² can be constructed by the use of the trace anomaly equation and tells us that magnetic gluon condensation, 〈0|(F_μν^a)²|0〉 > 0, occurs. When the method is applied to supersymmetric QCD, however, it gives us a puzzle; the gluons condense with negative energy density, and supersymmetry is broken in a pathological manner with the appearance of a negatively normed Nambu-Goldstone fermion. Spurred on by this observation, we examine in detail the properties of the vacuum for the super (and ordinary) O(N) non-linear σ model in two dimensions for which a similar puzzling situation occurs with regard to the lagrangian condensate. We find, in particular, that (i) the chiral condensate plays a crucial role in resolving the puzzle and that (ii) it is the nature of the response of the lagrangian condensate to the test charge, not the sign or the magnitude of the condensate itself, that determines the phase of the system. Implications of these results for (super) QCD, including an unconventional possibility of “electric” gluon condensation, are discussed.     

Neutrino oscillations from supersymmetry without R-parity—its implications on the flavor structure of the theory

We discuss here some flavor structure aspects of the complete theory of supersymmetry without R-parity addressed from the perspective of fitting neutrino oscillation data based on the recent Super-Kamiokande result. The single-VEV parameterization of supersymmetry without R-parity is first reviewed, illustrating some important features not generally appreciated. For the flavor structure discussions, a naive, flavor-model-independent, analysis is presented, from which a few interesting things can be learned.     

Neutrino mass and magnetic moment in supersymmetry without R-parity in the light of recent data

We consider the generation of neutrino Majorana mass and transition magnetic moment by the lepton-number violating λ and/or λ′ couplings in R-parity-violating supersymmetric models. We update (and improve) the existing upper limits on the relevant couplings using the most recent data on neutrino masses and mixings, indicating also the possible improvement by the GENIUS project. We study the implication of this update on the induced neutrino magnetic moment.     

Fractional supersymmetry as a superposition of ordinary supersymmetry

It is shown how to derive fractional supersymmetric quantum mechanics of order k as a superposition of k-1 copies of ordinary supersymmetric quantum mechanics.     

Unconstrained supersymmetry

This is a first step towards better superfield formulations of supersymmetric field theories. The simple Wess-Zumino model (including renormalizable interactions) is formulated in terms of an unconstrained, scalar superfield, obeying a wave equation that includes the square of the super Klein-Gordon operator. This wave equation is derived from an action principle, by unconstrained variation of the superfield. The physical content of the theory is the same as for the original formulation by Wess and Zumino, and the Feynman rules are identical to those of Grisaru, Roek and Siegel. Next, super electrodynamics, including minimal interactions with a scalar matter multiplet, is given a similar treatment. There is no need, in this case, to include higher derivatives in the Lagrangian. The matter field is an unconstrained, scalar superfield, and the gauge fields are also contained in an unconstrained, scalar superfield. The scattering matrix coincides with that of the conventional form of super electrodynamics with Wess-Zumino matter fields. Supersymmetric spinorial currents are found by simple and direct application of the Noetherian method, in superfield language. Conservation laws of the formD _a J ^a =0 (resp.D _a J ^ab =0) are derived from gauge invariance (resp. supersymmetry). Extension to super Yang-Mills theories is straightforward.On leave of absence from Universidad Complutense, Madrid. Permanent address: Department of Theoretical Physics, Universidad Complutense, 28040 Madrid, Spain.     

Low-energy supersymmetry

We discuss the problem of constructing a model in which supersymmetry is unbroken down to low energies. It is suggested that the scalar partners of quarks and leptons may get their masses through radiative corrections and that the breaking of the weak interactions also occurs through radiative corrections. A toy model is constructed which illustrates these ideas.     

Secret supersymmetry

We present new non-linear realizations of the N = 1 supergravity algebra. They allow us to build interesting realistic models of the four forces of nature. These models are different from all previous ones in that particles do not appear in (broken) supersymmetric multiplets.These new non-linear realizations also permit us to construct the effective low-energy lagrangian of an arbitrary supergravity theory in which supersymmetry is spontaneously broken. We are thus able to analyze what are the model-independent low-energy effects of supergravity. We find that the number of Higgs fields and the way they couple to quark and lepton matter is a feature which distinguishes supersymmetric theories from non-supersymmetric ones.     

Diffusive Limits on the Penrose Tiling

In this paper random walks on the Penrose lattice are investigated. Heat kernel estimates and the invariance principle are shown.     

Measuring supersymmetry

If new physics is found at the LHC (and the ILC) the reconstruction of the underlying theory should not be biased by assumptions about high-scale models. For the mapping of many measurements onto high-dimensional parameter spaces we introduce SFitter with its new weighted Markov chain technique. SFitter constructs an exclusive likelihood map, determines the best-fitting parameter point and produces a ranked list of the most likely parameter points. Using the example of the TeV-scale supersymmetric Lagrangian we show how a high-dimensional likelihood map will generally include degeneracies and strong correlations. SFitter allows us to study such model-parameter spaces employing Bayesian as well as frequentist constructions. We illustrate in detail how it should be possible to analyze high-dimensional new-physics parameter spaces like the TeV-scale MSSM at the LHC. A combination of LHC and ILC measurements might well be able to completely cover highly complex TeV-scale parameter spaces.     

Hidden supersymmetry

Inspired by the concept of complementarity, we present a illustrative model for the weak interactions with unbroken gauge symmetry and unbroken supersymmetry. The observable particles are bound states of some more fundamental particles. Supersymmetry is broken at the macroscopic scale of the observable particles by a discrete symmetry but remains exact at the scale of the fundamental particle and is thus hidden. This provides a link between theories at very high energies and the observed particle physics. Supersymmetric particles are confined in usual matter.     

Radiative transfer in plane media without azimuthal symmetry

A rigorous integral theory is presented in this paper for the solution of radiative heat transfer problems in stratified media, when dependence on the azimuth of the propagating radiation must be taken into account. Anisotropy of scattering and specular and diffuse reflection from the bounding walls are incorporated in the final system of linear integral equations of Fredholm's type. A simple case of physical interest is considered in more detail, and solved explicitly by a constructive technique. Numerical results are reported and briefly discussed.