Supersymmetry in the interacting boson fermion model as a formal property of a schwinger-type boson-fermion mapping

We investigate a SO(4) model with two one-dimensional collective pairs. We demonstrate how the whole model Hilbert space, including collective and noncollective states, can be mapped exactly on a space of bosons and fermions. We find a conservation law for the total number of bosons plus fermions that strongly resembles supersymmetry schemes as they are presently discussed in the framework of the interacting boson fermion model.     

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.     

Books received

This article is a colloquium-level review of the idea of supersymmetry and why so many physicists expect it to soon be a major discovery in particle physics. Supersymmetry is the hypothesis, for which there is indirect evidence, that the underlying laws of nature are symmetric between matter particles (fermions) such as electrons and quarks, and force particles (bosons) such as photons and gluons.     

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.     

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.     

Gauge-invariant effective lagrangians for goldstone-like particles of supersymmetric technicolor models

We point out that generally the low-energy spectrum in supersymmetric technicolor models contains quasi-Goldstone fermions and quasi-Goldstone bosons in addition to the usual (pseudo)- Goldstone bosons. Using the language of Kähler geometry, we present a step-by-step procedure for constructing gauge-invariant non-linear lagrangians involving the fermionic and bosonic Goldstone particles in situations in which supersymmetry is preserved. Both the cases of fully gauged and partially gauged global symmetries are considered. We discuss the dynamical version of the super-Higgs mechanism, and we illustrate it with the supersymmetric Susskind-Weinberg technicolor model.     

Exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions

The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with δ-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the SU(2|2) supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.     

Spontaneous supersymmetry breaking and superconductivity in a non-relativistic model

The conjecture that supersymmetry breaking implies superconductivity is supported by the analysis of a class of supersymmetric non-relativistic models involving only fermions. Here the investigation is extened to a non-relativistic model involving both fermions and bosons, which in a sense is the non-relativistic version of the Wess-Zumino model. A sufficient condition is established for the validity of the conjecture. This condition can be possibly violated at most in a two-dimensional subspace of the three-dimensional space of the coupling constants.     

Dynamical Field Inference and Supersymmetry

Knowledge on evolving physical fields is of paramount importance in science, technology, and economics. Dynamical field inference (DFI) addresses the problem of reconstructing a stochastically-driven, dynamically-evolving field from finite data. It relies on information field theory (IFT), the information theory for fields. Here, the relations of DFI, IFT, and the recently developed supersymmetric theory of stochastics (STS) are established in a pedagogical discussion. In IFT, field expectation values can be calculated from the partition function of the full space-time inference problem. The partition function of the inference problem invokes a functional Dirac function to guarantee the dynamics, as well as a field-dependent functional determinant, to establish proper normalization, both impeding the necessary evaluation of the path integral over all field configurations. STS replaces these problematic expressions via the introduction of fermionic ghost and bosonic Lagrange fields, respectively. The action of these fields has a supersymmetry, which means there exists an exchange operation between bosons and fermions that leaves the system invariant. In contrast to this, measurements of the dynamical fields do not adhere to this supersymmetry. The supersymmetry can also be broken spontaneously, in which case the system evolves chaotically. This affects the predictability of the system and thereby makes DFI more challenging. We investigate the interplay of measurement constraints with the non-linear chaotic dynamics of a simplified, illustrative system with the help of Feynman diagrams and show that the Fermionic corrections are essential to obtain the correct posterior statistics over system trajectories.     

Anomaly cancellations in the local supersymmetric Siegel lagrangian

The local supersymmetric Siegel action for two-dimensional chiral bosons and fermions is studied. It is found that the theory has local supersymmetry anomalies as well as gravitational-like anomalies. A modification of the lagrangian yielding anomaly cancellations is obtained.     

SUSY searches at ATLAS

Despite the absence of experimental evidence, weak scale supersymmetry remains one of the best motivated and studied Standard Model extensions. The ATLAS experiment at the LHC searches for signs of supersymmetry in a large variety of signatures involving events with abnormal production of missing transverse momentum, jets, leptons, third generation fermions, gauge bosons or massive long-lived particles. A summary of the most recent results obtained in these searches is presented.     

Coherence properties of two trapped particles

We analyse the coherence properties of two particles trapped in a one-dimensional harmonic potential. This simple model allows us to derive analytic expressions for the first and second order coherence functions. We investigate their properties depending on the particle nature and the temperature of the quantum gas. We find that at zero temperature non-interacting bosons and fermions show very different correlations, while they coincide for higher temperatures. We observe atom bunching for bosons and atom anti-bunching for fermions. When the effect of s-wave scattering between bosons is taken into account, we find that the range of coherence is enhanced or reduced for repulsive or attractive potentials, respectively. Strongly repelling bosons become in some way more “fermion-like" and show anti-bunching. Their first order coherence function, however, differs from that for fermions. Received 19 September 2002 Published online 4 February 2003     

Spontaneous Lorentz violation via QED with non-exact gauge invariance

We reconsider an alternative theory of QED with the photon as a massless vector Nambu–Goldstone boson and show that the underlying spontaneous Lorentz violation caused by the vector field vacuum expectation value, while being superficial in gauge invariant theory, becomes physically significant in QED with a tiny gauge non-invariance. This leads, through special dispersion relations appearing for charged fermions, to a new class of phenomena, which could be of distinctive observational interest in particle physics and astrophysics. They include a significant change in the GZK cutoff for UHE cosmic-ray nucleons, stability of high-energy pions and W bosons, a modification of nucleon beta decays, and some other ones.     

Spin and statistics in massive (2+1)-dimensional QED

We reexamine the questions of spin and statistics of nonrelativiic charged particles coupled to a topologically massive abelian gauge field. We show that these particles obey fractional statistics and carry an extra (gauge invariant) spin so that the generalized spin statistics relation is fulfilled. In particular, if the topological mass is obtained from integrating out heavy fermion fields, two flavors of fermions are needed to turn bosons into fermions. We also show, by explicitly considering the Dirac vacuum in the presence of a heavy point particle, that screening charge is exponentially localized and that the fermions do not contribute to the (gauge invariant) spin of the particle.     

Some fermi surface properties of double-exchange interaction systems

We study the photoemission spectrum of the double-exchange (DE) interaction systems. The DE Hamiltonian can be transformed into a simple form consisting of fermions and Schwinger bosons. We apply the gauge-field model and calculate the Green's function of the gauge field, fermions, and bosons. The imaginary part of the Green's function of an electron has an asymmetrical peak with strong temperature dependence. This can explain why the shape of the angle-resolved photoemission spectra of manganites near the Fermi surface is very different from that of Fermi liquid. We also show why the position of the Fermi surface is not sensitive to temperature.     

Dynamics of O(N) chiral supersymmetry at finite energy density

We consider an O(N) version of a massive, interacting, chiral supersymmetry model solved exactly in the large N limit. We demonstrate that the system approaches a stable attractor at high energy densities, corresponding to a non-perturbative state for which the relevant field quanta are massless. The state is one of spontaneously broken O(N), which, due to the influence of supersymmetry, does not become restored at high energies. Introducing soft supersymmetry breaking to the Lagrangian results in scalar masses at the soft breaking scale m_s independent of the mass scale of supersymmetry μ, with even smaller masses for the fermions.     

Superconducting strings

It is known that certain spontaneously broken gauge theories give rise to stable strings or vortex lines. In this paper it is shown that under certain conditions such strings behave like superconducting wires whose passage through astrophysical magnetic fields would generate a variety of striking and perhaps observable effects. The superconducting charge carriers may be either bosons (if a charged Higgs field has an expectation value in the core of the string) or fermions (if charged fermions are trapped in zero modes along the string, as is known to occur in certain circumstances). They might be observable as synchrotron sources or as sources of high-energy cosmic rays. If the charge carriers are ordinary quarks and leptons, the strings have important baryon number violating interactions with magnetic fields; such a string, traversing a galactic magnetic field of 10^?6 G, creates baryons (or antibaryons) at a rate of order 10¹² particles/cm of string per second.     

Finite supersymmetry transformations

We investigate simple examples of supersymmetry algebras with real and Grassmann parameters. Special attention is paid to the finite supertransformations and their probability interpretation. Furthermore we look for combinations of bosons and fermions which are invariant under supertransformations. These combinations correspond to states that are highly entangled.Received: 30 January 2004, Published online: 23 April 2004N. Ilieva: On leave from Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Boul. Tzarigradsko Chaussee 72, 1784 Sofia, Bulgaria     

Spontaneous supersymmetry breaking induced by vacuum condensates

We propose a novel mechanism of spontaneous supersymmetry breaking which relies upon a ubiquitous feature of Quantum Field Theory, vacuum condensates. Such condensates play a crucial role in many phenomena. Examples include Unruh effect, superconductors, particle mixing, and quantum dissipative systems. We argue that in all these phenomena supersymmetry, when present, is spontaneously broken. Evidence for our conjecture is given for the Wess–Zumino model, that can be considered as an approximation to the supersymmetric extensions of the above mentioned systems. The magnitude of the effect is estimated for a recently proposed experimental setup based on an optical lattice.     

τ→ν3π and the A1 resonance

We consider the possibility that the family group may be a spontaneously broken continuous global symmetry. In the context of grand unification, the couplings of the associated Goldstone bosons to fermions can be sufficiently suppressed so as to satisfy the phenomenological bounds. For a maximal family symmetry this requires a large number of Higgs fields.