Stable SU Research Articles

Stable Solutions to the Abelian Yang–Mills–Higgs Equations on $$S^2$$ and $$T^2$$

We show under natural assumptions that stable solutions to the abelian Yang–Mills–Higgs equations on Hermitian line bundles over the round 2-sphere actually satisfy the vortex equations, which are a first-order reduction of the (second-order) abelian Yang–Mills–Higgs equations. We also obtain a similar result for stable solutions on a flat 2-torus. Our method of proof comes from the work of Bourguignon–Lawson (Commun Math Phys 79(2):189–230, 1981) concerning stable SU(2) Yang–Mills connections on compact homogeneous 4-manifolds.

Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions

We report on the direct observation of spin-exchanging interactions in a two-orbital SU(N)-symmetric quantum gas of ytterbium in an optical lattice. The two orbital states are represented by two different (meta-)stable electronic configurations of fermionic Yb-173. A strong spin-exchange between particles in the two separate orbitals is mediated by the contact interaction between atoms, which we characterize by clock shift spectroscopy in a 3D optical lattice. We find the system to be SU(N)-symmetric within our measurement precision and characterize all relevant scattering channels for atom pairs in combinations of the ground and the excited state. Elastic scattering between the orbitals is dominated by the antisymmetric channel, which leads to the strong spin-exchange coupling. The exchange process is directly observed, by characterizing the dynamic equilibration of spin imbalances between two large ensembles in the two orbital states, as well as indirectly in atom pairs via interaction shift spectroscopy in a 3D lattice. The realization of a stable SU(N)-symmetric two-orbital Hubbard Hamiltonian opens the route towards experimental quantum simulation of condensed-matter models based on orbital interactions, such as the Kondo lattice model.

SU(5) heterotic Standard Model bundles

We construct a class of stable SU(5) bundles on an elliptically fibered Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass fibration, which admits a free involution. The bundles are invariant under the involution, solve the topological constraint imposed by the heterotic anomaly equation and give three generations of Standard Model fermions after symmetry breaking by Wilson lines of the intermediate SU(5) GUT-group to the Standard Model gauge group. Among the solutions we find some which can be perturbed to solutions of the Strominger system. Thus these solutions provide a step toward the construction of phenomenologically realistic heterotic flux compactifications via non-Kahler deformations of Calabi-Yau geometries with bundles. This particular class of solutions involves a rank two hidden sector bundle and does not require background fivebranes for anomaly cancellation.

Higgs multiplets in heterotic GUT models

For supersymmetric GUT models from heterotic string theory, built from a stable holomorphic SU(n) vector bundle $V$ on a Calabi-Yau threefold $X$, the net amount of chiral matter can be computed by a Chern class computation. Corresponding computations for the number $N_H$ of Higgses lead for the phenomenologically relevant cases of GUT group SU(5) or SO(10) to consideration of the bundle $\La^2 V$. In a class of bundles where everything can be computed explicitly (spectral bundles on elliptic $X$) we find that the computation for $N_H$ gives a result which is in conflict with expectations. We argue that this discrepancy has its origin in the subtle geometry of the spectral data for $\La^2 V$ and that taking this subtlety into account properly should resolve the problem.

On heterotic model constraints

The constraints imposed on heterotic compactifications by global consistency and phenomenology seem to be very finely balanced. We show that weakening these constraints, as was proposed in some recent works, is likely to lead to frivolous results. In particular, we construct an infinite set of such frivolous models having precisely the massless spectrum of the MSSM and other quasi-realistic features. Only one model in this infinite collection (the one constructed in [8]) is globally consistent and supersymmetric. The others might be interpreted as being anomalous, or as non-supersymmetric models, or as local models that cannot be embedded in a global one. We also show that the strongly coupled model of [8] can be modified to a perturbative solution with stable SU(4) or SU(5) bundles in the hidden sector. We finally propose a detailed exploration of heterotic vacua involving bundles on Calabi-Yau threefolds with 6 Wilson lines; we obtain many more frivolous solutions, but none that are globally consistent and supersymmetric at the string scale.

Deformations of bundles and the Standard Model

We modify a recently proposed heterotic model hep-th/0703210, giving three net-generations of Standard Model fermions, to get rid of an additional U(1) factor in the gauge group. The method employs a stable SU(5) bundle on a Calabi–Yau threefold admitting a free involution. The bundle has to be built as a deformation of the direct sum of a stable SU(4) bundle and the trivial line bundle.

Heat Transfer Nanofluids Based on Carbon Nanotubes

In this paper, we report the effort to prepare a stable su spension of carbon nanotube s in a hydro philic thermal transfer fluid with the motivation of enhancing its properties such as thermal conductivity and freezing point . The process of creating these fluid s involves the dispersion of carbon nanoparticles into the thermal transport fluid through intermittent sonication and the use of additives such as surfactants. I. Nomenclature

Maximized orbital and spin Kondo effects in a single-electron transistor

We investigate the charge fluctuations of a single-electron box (metallic grain) coupled to a lead via a smaller quantum dot in the Kondo regime. The most interesting aspect of this problem resides in the interplay between spin Kondo physics stemming from the screening of the spin of the small dot and orbital Kondo physics emerging when charging states of the grain with (charge) Q=0 and Q=e are almost degenerate. Combining Wilson's numerical renormalization-group method with perturbative scaling approaches we push forward our previous work [K. Le Hur and P. Simon, Phys. Rev. B 67, 201308R (2003)]. We emphasize that for symmetric and slightly asymmetric barriers, the strong entanglement of charge and spin flip events in this setup inevitably results in a non trivial stable SU(4) Kondo fixed point near the degeneracy points of the grain. By analogy with a small dot sandwiched between two leads, the ground state is Fermi-liquid like which considerably smears out the Coulomb staircase behavior and hampers the Matveev logarithmic singularity to arise. Most notably, the associated Kondo temperature $T_K^{SU(4)}$ might be raised compared to that in the conductance experiments through a small quantum dot $(\sim 1K)$ which makes the observation of our predictions a priori accessible. We discuss the robustness of the SU(4) correlated state against the inclusion of an external magnetic field, a deviation from the degeneracy points, particle-hole symmetry in the small dot, asymmetric tunnel junctions and comment on the different crossovers.

Smearing of charge fluctuations in a grain by spin-flip assisted tunneling

We investigate the charge fluctuations of a grain coupled to a lead via a small quantum dot in the Kondo regime. We show that the strong entanglement of charge and spin flips in this setup results in a stable SU(4) Kondo fixed point, which considerably smears out the Coulomb staircase behavior already in the weak-tunneling limit. This behavior is robust enough to be experimentally observable.

Vector Bundle Moduli and Small Instanton Transitions

We give the general presciption for calculating the moduli of irreducible, stable SU(n) holomorphic vector bundles with positive spectral covers over elliptically fibered Calabi-Yau threefolds. Explicit results are presented for Hirzebruch base surfaces B=F_r. The transition moduli that are produced by chirality changing small instanton phase transitions are defined and specifically enumerated. The origin of these moduli, as the deformations of the spectral cover restricted to the ``lift'' of the horizontal curve of the M5-brane, is discussed. We present an alternative description of the transition moduli as the sections of rank n holomorphic vector bundles over the M5-brane curve and give explicit examples. Vector bundle moduli appear as gauge singlet scalar fields in the effective low-energy actions of heterotic superstrings and heterotic M-theory.

Spin and dualization ofSU(5)dyons

Motivated by the dual standard model, we study the angular momentum spectrum of stable SU(5) dyons that can be transformed into purely electric states by a suitable duality rotation i.e. are dualizable. The problem reduces to solving a Diophantine equation for the holomorphic charges in each topological sector, but the solutions also have to satisfy certain constraints. We show that these equations can be solved and sets of dualizable, half-integer spin SU(5) dyons can be found, each of which corresponds to a single family of the standard model fermions. We then find two predictions of the dual standard model. First, the family of half-integer spin, dualizable dyons is accompanied by a set of dualizable, integer-spin partner states. Secondly, the dyon corresponding to the electron must necessarily contain non-trivial color internal structure. In addition, we provide other general results regarding the spectrum of dualizable dyons and their novel properties, and extend the stability analysis of SU(5) monopoles used in the dual standard model so far to discuss the stability of the half-integer spin dyons.

Explicit construction of nontrivial elements for homotopy groups of classical Lie groups

Nontrivial elements of homotopy groups for unitary, orthogonal, and symplectic groups are given explicitly. In particular, (a) representatives of generators of nontrivial homotopy groups of stable special unitary, orthogonal, and symplectic groups are constructed using Clifford algebras; (b) the values for ‘‘winding numbers’’ for stable SU, SO, and Sp are calculated for generators of homotopy groups; and (c) representatives of generators of homotopy groups Πn−2(O(n−1)), Π2n−2(U(n−1)), Π4n−2(Sp(n−1)) are given.

Stable SU(5) monopoles with higher magnetic charge.

Taking into account the electroweak breaking effects, some multiply charged monopoles were shown to be stable by Gardner and Harvey. We give the explicit Ansa$uml---tze for finite-energy, nonsingular solutions of these stable higher-strength monopoles with eg=1,(3/2),3. We also give the general stability conditions and the detailed behavior of the interaction potentials between two monopoles which produce the stable higher-strength monopoles.

Gauge-invariant analysis of spontaneous symmetry breaking of an SU(5) adjoint scalar model.

A Monte Carlo calculation is performed for a theory of SU(5) gauge fields interacting with adjoint scalar matter fields. The tree-level scalar potential is chosen to break SU(5) to SU(3) \ensuremath{\bigotimes} SU(2) \ensuremath{\bigotimes} U(1), but it is found that radiative corrections due to the gauge bosons give rise to the possibility of breaking to a metastable (perhaps even stable) SU(4) \ensuremath{\bigotimes} U(1) phase for certain ranges of the bare scalar mass. The transitions between the various phases of the theory are found to be first order. The implications of these results for continuum physics are as yet unclear.