Fermionic composite models from confining SU(2)L

A class of fermionic composite models with SU(2)_L as confining group is discussed utilizing the notion of complementarity. The models are, in some sense, fermionic realizations of the bosonic Abbott-Farhi model, avoiding fundamental scalars. Model A has SU(2)_L as confining group; model B has an additional chiral SU(M) and coincides with a model by Abbott, Fahri and Schwimmer; model C has an additional vector SU(M) and provides for a closer realization of the original basonic model.     

Realization of a SU(2)×SU(6) system of fermions in a cold atomic gas

We report the realization of a novel degenerate Fermi mixture with an SU(2)×SU(6) symmetry in a cold atomic gas. We successfully cool the mixture of the two fermionic isotopes of ytterbium 171Yb with the nuclear spin I=1/2 and 173Yb with I=5/2 below the Fermi temperature T_{F} as 0.46TF for 171Yb and 0.54TF for 173Yb. The same scattering lengths for different spin components make this mixture featured with the novel SU(2)×SU(6) symmetry. The nuclear spin components are separately imaged by exploiting an optical Stern-Gerlach effect. In addition, the mixture is loaded into a 3D optical lattice to implement the SU(2)×SU(6) Hubbard model. This mixture will open the door to the study of novel quantum phases such as a spinor Bardeen-Cooper-Schrieffer-like fermionic superfluid.     

Symmetric versus antisymmetric mass matrices in grand unified theories

We point out some interesting consequences of antisymmetric fermionic mass terms in grand unified theories, which follow from the symmetry properties of the Yukawa-type fermion-Higgs interactions. In SU(5), we show that an antisymmetric mass matrix M(u) in the up-quark sector arises when the Higgs 5 is replaced by 45. IOn SO(10), all the fermion sectors are characterized by such mass matrices if the neutrinos are required not to pick up the ordinary fermionic mass scale. In the recently proposed vertical-horizontal symmetric SU(5) × SU(5) scheme, a fully antisymmetric M(u) is naturally accompanied by exactly five zeroth-order massless neutrinos.     

Exactly solvable model for isospin S=3/2 fermionic atoms on an optical lattice

We propose an exact solution of a model describing a low energy behavior of cold isospin S=3/2 fermionic atoms on a one-dimensional optical lattice. Depending on the band filling the effective field theory has a form of a deformed Gross-Neveu model with either O(7)x Z2 (half filling) or U(1) x O(5) x Z2 symmetry.     

Path-integral formulation of two-dimensional gauge theories with massless fermions

We study (1 + 1) dimensional gauge theories [with SU(N) and diagonal SU(N) color symmetry] using the functional integral method. We construct an effective lagrangian by performing a change in the fermionic variables, and then investigate relevant phenomena such as the intrinsic Higgs mechanism and color screening.     

Supersymmetry in the problem of a fermion in an external nonabelian gauge field

The quantum-mechanical problem was considered of the motion of a Dirac particle in a nonabelian chromomagnetic field of the local isospin group SU(2). It was shown that the problem possesses supersymmetry. Supercharges were constructed, satisfying the standard superalgebra. The fermionic number operator coincides with the invariant spin operator of the Dirac equation. We clarified the features, in the given case, of supersymmetry, appearing in the anomaly of the commutation relations for the bosonic operators that was caused by the mutual tie of the bosonic (spatial and isospin) and the fermionic (spin) degrees of freedom for motion in the gauge field considered. It was demonstrated that the degeneracy of the vacuum (ground state) is removed by means of the spontaneous symmetry-breaking SU(2)U(1). The choice of a solution in the group U(1) is determined by the sign of the charge (color) of the particle in the ground state.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 40–44, February, 1989.     

Gauged Goldstone boson effective action from direct integration of bardeen anomaly

We derive the effective action which describes the anomalous Goldstone boson interactions in the presence of external flavour SU(N)_L×SU(N)_R gauge fields, by a direct integration of the Bardeen anomaly. Through comparison with other results, we are able to elucidate the relationship between anomalies based on different regularization schemes. We also give a compact representation of the anomalous part of the fermionic determinant allowing for a simpler rederivation of our results.     

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.     

Symmetry properties of the pomeron for t≠0

We investigated the SU(3) character of vacuum exchange amplitudes for πN, KN elastic scattering and for vector-meson photoproduction. Support is found for the recently proposed view that the single component becomes increasingly dominant away from t = 0, and that the eikonal amplitude is the quantity to which the symmetry breaking predictions seem to apply.     

Solution of the SU(2)q invariant XY-Model

We consider the SU(2)q invariant version of the XY-Model, present its solution for a chain of lengthN and its relation to the XY-Model with open boundary conditions for a chain of lengthN-1, construct the representation of the generalized spin operators by fermionic operators and discuss the SU(2)q multiplets. We determine the energies of the groundstates in the subspaces with fixed spin, compare them with results for the XY-Models with periodic and open boundary conditions and extract the central charge.     

Coherent states and quantum oscillations of BEC-BCS systems

We show by using the mean-field approximation that the states of composite Fermi-Bose superfluids created in cold-atom traps via a Feshbach resonance at zero temperature are generalized SU(2)⊗SU(1,1) coherent states. In response to a sudden change of the interaction between fermionic atoms and bosonic molecules, a Cooper pair can exhibit collapse and revival quantum behaviors for an initial generalized coherent state of molecules, and Rabi oscillation for a vacuum molecular state. Occurrence of the collapse and revival phenomenon is thus the manifestation of the formation of the Bose-Einstein condensate.     

Quantization of superparametrized monopoles

Classical finite-energy solutions of the SU(2) Yang-Mills-Higgs system in four-dimensional space-time are embedded in the supersymmetric extension of the theory. Finite supertranslations are constructed and are used to obtain a family of solutions to the supersymmetric field equations, parametrized by fermionic Majorana spinor parameters. The quantum theory around arbitrary classical solutions, parametrized by arbitrary bosonic (global and local) as well as fermionic (global) parameters, is constructed and discussed.     

Universality of the string picture in lattice gauge systems

We test the conjecture that the infrared behaviour of gauge theories is described by an effective string picture by analyzing the Monte Carlo data of five different three- and four-dimensional lattice gauge systems, SU(2) and SU(3) included. We find that there is a unique string of fermionic type which fits well to the whole set of analyzed data.     

Confinement and superfluidity in one-dimensional degenerate fermionic cold atoms

The physical properties of arbitrary half-integer spins F = N - (1/2) fermionic cold atoms trapped in a one-dimensional optical lattice are investigated by means of a low-energy approach. Two different superfluid phases are found for F > or = (3/2) depending on whether a discrete symmetry is spontaneously broken or not: an unconfined BCS pairing phase and a confined molecular-superfluid instability made of 2N fermions. We propose an experimental distinction between these phases for a gas trapped in an annular geometry. The confined-unconfined transition is shown to belong to the Z(N) generalized Ising universality class. We discuss the possible Mott phases at (1/2) filling.     

Generations in the rishon model

We present a model for fermions composed of rishons in which colour plays a determinant role providing for only three generations. The couplings with the gauge bosons of the SU(2)_L × SU(2)_R × U(1)_B?L theory as well as with Higgs bosons are determined by the colour substructures. Two appealing possibilities emerge: the Cabibbo mixing angles could be small due to their dependence on the colour coupling constant and the fermionic mass hierarchy could be related to the fact that the products of higher representations have a richer decomposition allowing for the coupling with more Higgs fields.     

Twist deformations of the supersymmetric quantum mechanics

The $ \mathcal{N} $ \mathcal{N} -extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even $ \mathcal{N} $ \mathcal{N} one can identify the 1D $ \mathcal{N} $ \mathcal{N} -extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.     

Fermion condensation in the field strength approach to non-abelian yang-mills theories

Within the field strength approach to Yang-Mills theories the fermionic sectors of gauge theories are bosonized for the SU(2) and SU(3) gauge group. The emerging effective meson theories are studied in the tree approximation. In this approximation the original minimal gauge coupling of the quarks to gluons is rendered into an effective local four-fermion interaction with non-trivial Lorentz and gauge structure. The Schwinger-Dyson equation is solved in the strong coupling limit and the quark condensates and constituent masses are evaluated.     

Variational Stochastic Procedure for Broken Symmetry Phase and Fermionic Fields

Stochastic quantization of the O(N)⁴-field theory is studied in the brokensymmetry phase by a variational approach. The resultingintegral equation is solved analytically to any order in1/N expansion. This method is adapted to fermionic models. Inparticular, an analytic fermionic toy model isintroduced in D = 0 and we argue that the D-dimensionalcase is directly accessible in this way.     

Symmetry breaking of the symmetric left-right model without a scalar bidoublet

By invoking the existence of a general O(2) symmetry, a minimal left-right symmetric model based on the gauge group is shown to require the existence of only two physical Higgs bosons. The lighter Higgs is predicted to have a small mass which could be evaluated by standard perturbation theory. The fermionic mass matrices are recovered by insertion of ad hoc fermion-Higgs interactions. The model is shown to be undistinguishable from the standard model at the currently reachable energies.Received: 10 August 2003, Revised: 18 October 2003, Published online: 18 December 2003