Cancellation of quadratically divergent mass corrections in globally supersymmetric spontaneously broken gauge theories

The one-loop quadratically divergent mass corrections in globally supersymmetric gauge theories with spontaneously broken abelian and non-abelian gauge symmetry are studied. Quadratically divergent mass corrections are found to persist in an abelian model with an ABJ anomaly. However, additional supermultiplets necessary to cancel the ABJ anomaly, turn out to be sufficient to eliminate the quadratic divergences as well, rendering the theory natural. Quadratic divergences are shown to vanish also in the case of an anomaly free model with spontaneously broken non-abelian gauge symmetry.

Non-Abelian gauge redundancy and entropic ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. Therefore one reaches the remarkable possibility that there may be many entropies for a given state. We show that this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This ambiguity in entropy, which can occur at zero temperature, can often be traced to a gauge symmetry emergent from the non-trivial topological character of the configuration space of the underlying system. We also establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix. After demonstrating this entropy ambiguity for the simple example of the algebra of 2 x 2 matrices, we argue that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. We work out the simplest situation with such non-Abelian symmetry, that of an ethylene molecule.

Technicolor

The need for reexamination of the standard model of strong, weak, and electromagnetic interactions is discussed, especially with regard to 't Hooft's criterion of naturalness. It has been argued that theories with fundamental scalar fields tend to be unnatural at relatively low energies. There are two solutions to this problem: (i) a global supersymmetry, which ensures the absence of all the naturalness-violating effects associated with scalar fields, and (ii) composite structure of the scalar fields, which starts showing up at energy scales where unnatural effects would otherwise have appeared. With reference to the second solution, this article reviews the case for dynamical breaking of the gauge symmetry and the technicolor scheme for the composite Higgs boson. This new interaction, of the scaled-up quantum chromodynamic type, keeps the new set of fermions, the technifermions, together in the Higgs particles. It also provides masses for the electroweak gauge bosons W± and Z0 through technifermion condensate formation. In order to give masses to the ordinary fermions, a new interaction, the extended technicolor interaction, which would connect the ordinary fermions to the technifermions, is required. The extended technicolor group breaks down spontaneously to the technicolor group, possibly as a result of the "tumbling" mechanism, which is discussed here. In addition, the author presents schemes for the isospin breaking of mass matrices of ordinary quarks in the technicolor models. In generalized technicolor models with more than one doublet of technifermions or with more than one technicolor sector, we have additional low-lying degrees of freedom, the pseudo-Goldstone bosons. The pseudo-Goldstone bosons in the technicolor model of Dimopoulos are reviewed and their masses computed. In this context the vacuum alignment problem is also discussed. An effective Lagrangian is derived describing colorless low-lying degrees of freedom for models with two technicolor sectors in the combined limits of chiral symmetry and large number of colors and technicolors. Finally, the author discusses suppression of flavor-changing neutral currents in the extended technicolor models.

Quantum entropic ambiguities: Ethylene

In a quantum system, there may be many density matrices associated with a state on an algebra of observables. For each density matrix, one can compute its entropy. These are, in general, different. Therefore, one reaches the remarkable possibility that there may be many entropies for a given state R. Sorkin (private communication)]. This ambiguity in entropy can often be traced to a gauge symmetry emergent from the nontrivial topological character of the configuration space of the underlying system. It can also happen in finite-dimensional matrix models. In the present work, we discuss this entropy ambiguity and its consequences for an ethylene molecule. This is a very simple and well-known system, where these notions can be put to tests. Of particular interest in this discussion is the fact that the change of the density matrix with the corresponding entropy increase drives the system towards the maximally disordered state with maximum entropy, where Boltzman's formula applies. Besides its intrinsic conceptual interest, the simplicity of this model can serve as an introduction to a similar discussion of systems such as colored monopoles and the breaking of color symmetry.

Entropy of quantum states: Ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.

Quantum entropy for the fuzzy sphere and its monopoles

Using generalized bosons, we construct the fuzzy sphere S-F(2) and monopoles on S-F(2) in a reducible representation of SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent nonabelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.

Dynamical generation of flavour

We propose the generation of Standard Model fermion hierarchy by the extension of renormalizable SO(10) GUT with O(N (g) ) family gauge symmetry. In this scenario, Higgs representations of SO(10) also carry family indices and are called Yukawons. Vacuum expectation values of these Yukawon fields break GUT and family symmetry and generate MSSM Yukawa couplings dynamically. We have demonstrated this idea using Higgs irrep, ignoring the contribution of 1 2 0-plet which is, however, required for complete fitting of fermion mass-mixing data. The effective MSSM matter fermion couplings to the light Higgs pair are determined by the null eigenvectors of the MSSM-type Higgs doublet superfield mass matrix . A consistency condition on the doublet (1,2,+/- 1]) mass matrix ( 0) is required to keep one pair of Higgs doublets light in the effective MSSM. We show that the Yukawa structure generated by null eigenvectors of are of generic kind required by the MSSM. A hidden sector with a pair of (S (a b) ; I center dot (a b) ) fields breaks supersymmetry and facilitates 0. SUSY breaking is communicated via supergravity. In this scenario, matter fermion Yukawa couplings are reduced from 15 to just 3 parameters in MSGUT with three generations.

Role of polarization in probing anomalous gauge interactions of the Higgs boson

We explore the use of polarized e(+)/e(-) beams and/or the information on final state decay lepton polarizations in probing the interaction of the Higgs boson with a pair of vector bosons. A model independent analysis of the process e(+)e(-) -> f (f) over barH, where f is any light fermion, is carried out through the construction of observables having identical properties under the discrete symmetry transformations as different individual anomalous interactions. This allows us to probe an individual anomalous term independent of the others. We find that initial state beam polarization can significantly improve the sensitivity to CP-odd couplings of the Z boson with the Higgs boson (ZZH). Moreover, an ability to isolate events with a particular tau helicity, with even 40% efficiency, can improve sensitivities to certain ZZH couplings by as much as a factor of 3. In addition, the contamination from the ZZH vertex contributions present in the measurement of the trilinear Higgs-W (WWH) couplings can be reduced to a great extent by employing polarized beams. The effects of initial state radiation and beamstrahlung, which can be relevant for higher values of the beam energy are also included in the analysis.

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.

Bound states of two spin-1/2 fermions in a synthetic non-Abelian gauge field

We study the bound states of two spin-1/2 fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in three-dimensional space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba-type spin-orbit interaction is described by three coupling parameters (lambda(x),lambda(y),lambda(z)). For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is negative, i.e., shifts to the ``BCS side'' of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., lambda(x) = lambda(y) = lambda(z)) for which there is a two-body bound state for any scattering length however small and negative. Remarkably, the bound-state wave functions obtained for such configurations have nematic spin structure similar to those found in liquid He-3. Our results show that the BCS-BEC (Bose-Einstein condensation) crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.

BCS-BEC crossover induced by a synthetic non-Abelian gauge field

We investigate the ground state of interacting spin-1/2 fermions in three dimensions at a finite density (rho similar to k(F)(3)) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector lambda equivalent to (lambda(x),lambda(y),lambda(z)), whose magnitude lambda determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length (k(F)vertical bar a(s)vertical bar less than or similar to 1), the ground state in the absence of the gauge field (lambda = 0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum (lambda = 0). For large gauge couplings (lambda/k(F) >> 1), the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)-we call these bosons ``rashbons.'' In the absence of interactions (a(s) = 0(-)), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling lambda(T). For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of lambda near lambda(T). In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

Fermions in synthetic non-Abelian gauge potentials: rashbon condensates to novel Hamiltonians

Recent advances in the generation of synthetic gauge fields in cold atomic systems have stimulated interest in the physics of interacting bosons and fermions in them. In this paper, we discuss interacting two-component fermionic systems in uniform non-Abelian gauge fields that produce a spin-orbit interaction and uniform spin potentials. Two classes of gauge fields discussed include those that produce a Rashba spin-orbit interaction and the type of gauge fields (SM gauge fields) obtained in experiments by the Shanxi and MIT groups. For high symmetry Rashba gauge fields, a two-particle bound state exists even for a vanishingly small attractive interaction described by a scattering length. Upon increasing the strength of a Rashba gauge field, a finite density of weakly interacting fermions undergoes a crossover from a BCS like ground state to a BEC state of a new kind of boson called the rashbon whose properties are determined solely by the gauge field and not by the interaction between the fermions. The rashbon Bose-Einstein condensate (RBEC) is a quite intriguing state with the rashbon-rashbon interactions being independent of the fermion-fermion interactions (scattering length). Furthermore, we show that the RBEC has a transition temperature of the order of the Fermi temperature, suggesting routes to enhance the transition temperatures of weakly interacting superfluids by tuning the spin-orbit coupling. For the SM gauge fields, we show that in a regime of parameters, a pair of particles with finite centre-of-mass momentum is the most strongly bound. In other regimes of centre-of-mass momenta, there is no two-body bound state, but a resonance like feature appears in the scattering continuum. In the many-body setting, this results in flow enhanced pairing. Also, strongly interacting normal states utilizing the scattering resonance can be created opening the possibility of studying properties of helical Fermi liquids. This paper contains a general discussion of the physics of Feshbach resonance in a non-Abelian gauge field, where several novel features such as centre-of-mass-momentum-dependent effective interactions are shown. It is also shown that a uniform non-Abelian gauge field in conjunction with a spatial potential can be used to generate novel Hamiltonians; we discuss an explicit example of the generation of a monopole Hamiltonian.

A little more gauge mediation and the light Higgs mass

We consider minimal models of gauge mediated supersymmetry breaking with an extra U(1) factor in addition to the Standard Model gauge group. A U(1) charged, Standard Model singlet is assumed to be present which allows for an additional NMSSM like coupling, lambda HuHdS. The U(1) is assumed to be flavour universal. Anomaly cancellation in the MSSM sector requires additional coloured degrees of freedom. The S field can get a large vacuum expectation value along with consistent electroweak symmetry breaking. It is shown that the lightest CP even Higgs boson can attain mass of the order of 125 GeV. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/).

Feshbach resonance in a synthetic non-Abelian gauge field

We study the Feshbach resonance of spin-1/2 particles in a uniform synthetic non-Abelian gauge field that produces spin-orbit coupling and constant spin potentials. We develop a renormalizable quantum field theory including the closed-channel boson which engenders the resonance. We show that the gauge field shifts the Feshbach field where the low-energy scattering length diverges. In addition the Feshbach field is shown to depend on the center-of-mass momentum of the particles. For high-symmetry gauge fields which produce a Rashba spin coupling, we show that the system supports two bound states over a regime of magnetic fields when the background scattering length is negative and the resonance width is comparable to the energy scale of the spin-orbit coupling. We discuss interesting consequences useful for future theoretical and experimental studies, even while our predictions are in agreement with recent experiments.