Static SU Research Articles

Integral expression for a topological charge in the Faddeev–Niemi nonlinear sigma model

We have introduced Faddeev–Niemi type variables for static SU(3) Yang–Mills theory. The variables suggest that a nonlinear sigma model whose sigma fields take values in SU(3)/(U(1) × U(1)) and SU(3)/(SU(2) × U(1)) may be relevant to infrared limit of the theory. Shabanov showed that the energy functional of the nonlinear sigma model is bounded from below by certain functional. However, Shabanov’s functional is not homotopy invariant, and its value can be an arbitrary real number—therefore it is not a topological charge. Since the third homotopy group of SU(3)/(U(1) × U(1)) is isomorphic to the group of integer numbers, there is a non-trivial topological charge (given by the isomorphism). We apply Novikov’s procedure to obtain integral expression for this charge. The resulting formula is analogous to the Whitehead’s realization of the Hopf invariant.

The supersymmetric Wong equations and the non-abelian Landau problem

A Lagrangian formulation is given extending to supersymmetry, or the motion of a charged point particle with spin in a non-abelian external field. The classical formulation is constructed for any external static non-abelian SU(N) gauge potential. As an illustration, a specific gauge is fixed, enabling canonical quantization and the study of the supersymmetric non-abelian Landau problem. The spectrum of the quantum Hamiltonian operator follows in accordance with the supersymmetric structure.

Vortices and vortex states in Rashba spin-orbit-coupled condensates

The Rashba spin-orbit coupling is equivalent to the finite Yang-Mills flux of a static SU(2) gauge field. It gives rise to the protected edge states in two-dimensional topological band insulators, much like magnetic field yields the integer quantum Hall effect. An outstanding question is which collective topological behaviors of interacting particles are made possible by the Rashba spin-orbit coupling. Here we address one aspect of this question by exploring the Rashba SU(2) analogs of vortices in superconductors. Using the Landau-Ginzburg approach and conservation laws, we classify the prominent two-dimensional condensates of two- and three-component spin-orbit-coupled bosons, and characterize their vortex excitations. There are two prominent types of condensates that take advantage of the Rashba spin-orbit coupling. Their vortices exist in multiple flavors whose number is determined by the spin representation, and interact among themselves through logarithmic or linear potentials as a function of distance. The vortices that interact linearly exhibit confinement and asymptotic freedom similar to quarks in quantum chromodynamics. One of the two condensate types supports small metastable neutral quadruplets of vortices, and their tiles as metastable vortex lattices. Quantum melting of such vortex lattices could give rise to non-Abelian fractional topological insulators, SU(2) analogs of fractional quantum Hall states. The physical systems in which these states could exist are trapped two- and three-component bosonic ultracold atoms subjected to artificial gauge fields, as well as solid-state quantum wells made either from Kondo insulators such as ${\mathrm{SmB}}_{6}$ or conventional topological insulators interfaced with conventional superconductors.

New Faddeev-Niemi-Type variables for the static Yang-Mills theory

We propose new variables of Faddeev-Niemi type for static SU(3) Yang-Mills theory. These variables reveal a structure of a nonlinear sigma model, whose field variables are two chiral fields taking values in SU(3)/(U(1)xU(1)) and SU(3)/(SU(2)xU(1)). The nonlinear sigma model was introduced by Faddeev and Niemi as a natural extension of the Faddeev chiral model. Shabanov showed that the energy functional of the extended model is bounded from below by a topological invariant, and therefore may support knot-like excitations and a mass gap.

Effective theory of fractional topological insulators in two spatial dimensions

Electrons subjected to a strong spin-orbit coupling in two spatial dimensions could form fractional incompressible quantum liquids without violating the time-reversal symmetry. Here we construct a Lagrangian description of such fractional topological insulators by combining the available experimental information on potential host materials and the fundamental principles of quantum field theory. This Lagrangian is a Landau-Ginzburg theory of spinor fields, enhanced by a topological term that implements a state-dependent fractional statistics of excitations whenever both particles and vortices are incompressible. The spin-orbit coupling is captured by an external static SU(2) gauge field. The presence of spin conservation or emergent U(1) symmetries would reduce the topological term to the Chern-Simons effective theory tailored to the ensuing quantum Hall state. However, the Rashba spin-orbit coupling in solid-state materials does not conserve spin. We predict that it can nevertheless produce incompressible quantum liquids with topological order but without a quantized Hall conductivity. We discuss two examples of such liquids whose description requires a generalization of the Chern-Simons theory. One is an Abelian Laughlin-like state, while the other has a new kind of non-Abelian many-body entanglement. Their quasiparticles exhibit fractional spin-dependent exchange statistics, and have fractional quantum numbers derived from the electron's charge and spin according to their transformations under time-reversal. In addition to conventional phases of matter, the proposed topological Lagrangian can capture a broad class of hierarchical Abelian and non-Abelian topological states, involving particles with arbitrary spin or general emergent SU(N) charges.

Differential cross sections and recoil polarizations for the reactionγp→K+Σ0

High-statistics measurements of differential cross sections and recoil polarizations for the reaction $\gamma p \rightarrow K^+ \Sigma^0$ have been obtained using the CLAS detector at Jefferson Lab. We cover center-of-mass energies ($\sqrt{s}$) from 1.69 to 2.84 GeV, with an extensive coverage in the $K^+$ production angle. Independent measurements were made using the $K^{+}p\pi^{-}$($\gamma$) and $K^{+}p$($\pi^-, \gamma$) final-state topologies, and were found to exhibit good agreement. Our differential cross sections show good agreement with earlier CLAS, SAPHIR and LEPS results, while offering better statistical precision and a 300-MeV increase in $\sqrt{s}$ coverage. Above $\sqrt{s} \approx 2.5$ GeV, $t$- and $u$-channel Regge scaling behavior can be seen at forward- and backward-angles, respectively. Our recoil polarization ($P_\Sigma$) measurements represent a substantial increase in kinematic coverage and enhanced precision over previous world data. At forward angles we find that $P_\Sigma$ is of the same magnitude but opposite sign as $P_\Lambda$, in agreement with the static SU(6) quark model prediction of $P_\Sigma \approx -P_\Lambda$. This expectation is violated in some mid- and backward-angle kinematic regimes, where $P_\Sigma$ and $P_\Lambda$ are of similar magnitudes but also have the same signs. In conjunction with several other meson photoproduction results recently published by CLAS, the present data will help constrain the partial wave analyses being performed to search for missing baryon resonances.

Classes of AdS4type IIA/IIB compactifications with SU(3) × SU(3) structure

We introduce an ansatz which allows us to solve the supersymmetry equations for warped = 1 AdS4 type II supergravity compactifications of general SU(3) × SU(3) structure. As a byproduct we obtain a set of necessary conditions which every supersymmetric AdS4 vacuum should obey. The case of AdS4 compactifications of IIB on manifolds of static SU(2) structure is examined in detail. Several examples of solutions are presented. In the limit of four-dimensional Minkowski space, we present examples of supersymmetric IIB warped compactifications with partially localized NS5- and D5-branes. We also present `massive' non-supersymmetric AdS4 × 6 solutions of IIA, where 6 can be any six-dimensional Einstein-Kahler manifold.

Confinement and the second vortex of the SU(4) gauge group

We study the potential between static SU(4) sources using the model of thick center vortices. Such vortices are characterized by the center elements z{sub 1}=i and z{sub 2}=z{sub 1}{sup 2}. Fitting the ratios of string tensions to those obtained in Monte Carlo calculations of lattice QCD we get f{sub 2}>f{sub 1}{sup 2}, where f{sub n} is the probability that a vortex of type n is piercing a plaquette. Because of z{sub 2}=z{sub 1}{sup 2} vortices of type two are overlapping vortices of type one. Therefore, f{sub 2}>f{sub 1}{sup 2} corresponds to the existence of an attractive force between vortices of type one.

Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror hat M, it is argued that the product M × hat M is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and hat M. The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3) × SU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry.

Supersymmetric sources, integrability and generalized-structure compactifications

In the context of supersymmetric compactifications of type II supergravity to four dimensions, we show that orientifold sources can be compatible with a generalized SU(3) × SU(3)-structure that is neither strictly SU(3) nor static SU(2). We illustrate this with explicit examples, obtained by suitably T-dualizing known solutions on the six-torus. In addition we prove the following integrability statements, valid under certain mild assumptions: (a) for general type II supergravity backgrounds with orientifold and/or D-brane generalized-calibrated sources, the source-corrected Einstein and dilaton equations of motion follow automatically from the supersymmetry equations once the likewise source-corrected form equations of motion and Bianchi identities are imposed; (b) in the special case of supersymmetric compactifications to four-dimensional Minkowski space, the equations of motion of all fields, including the NSNS three-form, follow automatically once the supersymmetry and the Bianchi identities of the forms are imposed. Both (a) and (b) are equally valid whether the sources are smeared or localized. As a byproduct we obtain the calibration form for a space-filling NS5-brane.

A new lattice measurement for potentials between static SU(3) sources

In this article, a new calculation of static potentials between sources of different representations in SU(3) gauge group is presented. The results of author's previous study \cite{Deld00} at the smallest lattice spacing $a_{s}\simeq0.11$~ fm are shown to have been affected by finite volume effects. Within statistical errors, the new results obtained here are still in agreement with both, Casimir scaling and flux tube counting. There is also no contradiction to the results obtained in Ref.~ \cite{Bali00} which however exclude flux counting.

Finite temperature induced fermion number for quarks in a chiral field

We compute the finite temperature correction to the induced fermion number for fermions coupled to a static SU(2) chiral background, using the derivative expansion technique. At zero temperature the induced fermion number is topological, being the winding number of the chiral background. At finite temperature however, higher order terms in the derivative expansion give nontopological corrections to the winding number. We use this result to show that the standard cancellation of the fractional parts of the fermion number inside and outside the bag in an SU(2) x SU(2) hybrid chiral bag model of the nucleon does not occur at nonzero temperature.

Intrinsic polarized strangeness and $\Lambda ^0$ polarization in deep-inelastic production

We propose a model for the longitudinal polarization of Lambda baryons produced in deep-inelastic lepton scattering at any xF, based on static SU(6) quark-diquark wave functions and polarized intrinsic strangeness in the nucleon associated with individual valence quarks. Free parameters of the model are fixed by fitting NOMAD data on the longitudinal polarization of Lambda hyperons in neutrino collisions. Our model correctly reproduces the observed dependences of Lambda polarization on the kinematic variables. Within the context of our model, the NOMAD data imply that the intrinsic strangeness associated with a valence quark has anticorrelated polarization. We also compare our model predictions with results from the HERMES and E665 experiments using charged leptons. Predictions of our model for the COMPASS experiment are also presented.

Potentials between static SU(3) sources in the fat-center-vortices model

The potentials between static sources in various representaions in SU(3) are calculated based on the fat-center-vortices model of Faber, Greensite and Olejnik. At intermediate distances, most distributions of the flux within vortices lead to potentials that are qualitatively in agreement with ``Casimir scaling,'' which says that the string tension is proportional to the quadratic operator of the representation. However, at the quantitative level, violations of Casimir scaling are generally much larger than those seen in numerical simulations, indicating that additional physical input to the fat-center-vortices model is required. At large distances, screening occurs for zero-triality representations; for the representations with non-zero triality the string tension equals that of the fundamental representation. Some rather ``unphysical,'' flux distributions can lead to violations of Casimir scaling at intermediate distances and violations of the expected ordering of representations at large distances.

Slowly Rotating Non-Abelian Black Holes

It is shown that the well-known non-Abelian static SU(2) black hole solutions have rotating generalizations, provided that the hypothesis of linearization stability is accepted. Surprisingly, this rotating branch has an asymptotically Abelian gauge field with an electric charge that is proportional to the angular momentum, although the nonrotating limit is uncharged. We argue that this may be related to our second finding, namely that there are no globally regular slowly rotating excitations of the particlelike Bartnik-McKinnon solutions.

Reliable predictions in exclusive rare B decays

We discuss the relations between form factors for B→ K ∗γ and B→ ϱe ν which follow from static heavy quark symmetry methods plus SU(3). We discuss carefully the hard perturbative QCD corrections which could invalidate these results and find that the dominant perturbative corrections are ones which respect the static symmetry predictions, and in addition that the perturbative corrections are small compared to soft contributions. We show that there is a special kinematic point in B→ ϱe ν that involves the same combination of form factors as in B→ K ∗γ , thus allowing a prediction of the ratio of rates which is largely free from hadronic uncertainties.

Spherically symmetric static SU(2) Einstein–Yang–Mills fields

The discrete family of global solutions of the static spherically symmetric SU(2) Einstein–Yang–Mills equations that were recently numerically obtained by Bartnik and McKinnon [Phys. Rev. Lett. 61, 141 (1988)] is studied in greater detail, both numerically and analytically. A similar discrete sequence of numerical solutions outside a regular event horizon is shown to exist for every radius of the horizon.

Connection between the Einstein-Maxwell equations and the self-duality equations for gauge fields

An analysis is made of the possibility of the existence of a one-to-one correspondence between the Einstein-Maxwell equations and the self-duality equations for static axisymmetric SU(3) gauge fields in a gauge that reduces to the sigma-model representation on a noncompact symmetric space of the type AIII.

The adjoint source potential in SU(3) lattice gauge theory

The potential between static adjoint SU(3) colour sources is determined from pure gauge lattice Monte Carlo calculations. A linear component is found corresponding to an adjoint-to-fundamental string-tension ratio K A K F = 2.2 ±0.4 . We estimate that saturation of the adjoint potential occurs for separation R ≈ 7 GeV −1.

B�cklund transformations for static axially-symmetric self-dual SU(N) gauge fields

Backlund transformations are derived for static axially-symmetric self-dual SU(N) gauge fields. In the case of SU(3) broken to U(1) × U(1), they produce field configurations with fractional topological charges.