Fermion zero modes in the presence of non-abelian vortices

The Dirac equation in the presence of non-abelian vortices is investigated . For isospinor fermions coupled to the vortex in the SU(2) Nielsen-Olesen model, there are normalisable well-behaved zero-energy solutions. When the fermions are in the adjoint representation there are no normalisable zero modes. The Z₂ vortex appearing in a SO(10) theory is explicitly constructed and it is shown that the heavy neutrino can be bound to it in a zero-energy state.     

Moduli space of model real submanifolds

In [6], to a completely nondegenerate germ of a real submanifold of a chosen C R-type (n, K) in a complex space, we assigned a tangent polynomial model of the submanifold. In the present paper, we construct the moduli space M(n, K) of the family of polynomial models, i.e., the space parametrizing the holomorphically nonequivalent polynomial models. The space thus obtained is used to construct C R-characteristic classes. Financially supported by the RFBR grant no. 05-01-0981 and by the grant NSh-2040.2003.1.     

Composite coherence vortices and their propagation in free space

Taking Gaussian Schell-model (GSM) background vortex beams as an example of partially coherent vortex beams, the composite coherence vortices resulting from the superposition of the cross-spectral density function of two parallel, noncollinear partially coherent vortex beams and their propagation in free space are studied, and the main attention is paid to the effect of relative off-axis distance, coherence parameter and propagation distance on the composite coherence vortices. The number and location of composite coherence vortices vary by changing the relative off-axis distance, coherence parameter or propagation distance. In the coherent limit, the composite coherence vortex becomes the composite optical vortex.     

Moduli space for conifolds as intersection of orthogonal D6 branes

We show that a system of parallel D3 branes near a conifold singularity can be mapped onto an intersecting configuration of orthogonal branes in type IIA string theory. Using this brane configuration, we analyze the Higgs moduli space of the associated field theory. The dimension of the Higgs moduli space is computed from a geometrical analysis of the conifold singularity. Our results provide evidence for an extended s-rule. In addition, a discrepancy between the prediction of the brane configuration and the result obtained from a geometrical analysis is noted. This discrepancy can be traced back to worldsheet instanton effects.     

Conserved quantities for the geodesic motion on the configuration space of non-abelian Yang-Mills theory

We describe the geodesic motion on the configuration space of non-abelian Yang-Mills theories. We construct infinitely many integrals of the motion, and compute the Poisson brackets. We explicitly give infinitely many integrals in involution.     

Models of non-abelian orbifolds

Several models of non-abelian orbifolds have been constructed. There are models with three or four families of quarks and leptons, and gauge symmetry SU(3) × SU(2) × SU(2) × U(1)² × SU(3)′ × SO(10)′ × U(1)′ or SU(3) × SU(2) × U(1)³ × SU(4)′ × SO(8)′ × U(1)′.     

Some non-abelian Q-balls

Q-balls are a class of extended objects that arise in a large group of field theories with unbroken global symmetries. Earlier work investigated the properties of these objects for theories with abelian symmetries. We extend this work to some simple models with symmetry groups SO(3) and SU(3). We also develop parts of the theory of long-wavelength excitations of a general Q-ball.     

Transfer of angular momentum to matter from acoustical vortices in free space

An experimental demonstration of the mechanical transfer of orbital angular momentum to matter from acoustical vortices in free field is presented. Vortices with topological charges l=+/-1 and l=+/-2 were generated and a torsion pendulum was used to study the angular momentum transfer to hanging disks of several sizes. This allowed us to make a comparative study of the effective acoustical torque in terms of topological charge of the vortex, the disk radius, and its position along the main propagation axis. A theoretical discussion of the generated sound fields is also provided.     

Superposition of special non-abelian potentials

The superposition of the non-abelian potentials of the formA′^μ=Aα^μ+aβ ^μ andB′^μ=Bγ^μ+bη^μ are considered and the necessary as well as the sufficient conditions are obtained. The significance of the conditions is discussed and the constrained isotopic spins of the perturbation potentials (aβ ^μ,bη^μ) are shown to be necessary for the superposition of these potenitals. Work under the projecthcs/dst/1081/81     

Virial coefficients of non-abelian anyons

We study a system of non-Abelian anyons in the lowest Landau level of a strong magnetic field. Using diagrammatic techniques, we prove that the virial coefficients do not depend on the statistics parameter. This is true for all representations of all non-Abelian groups for the statistics of the particles and relies solely on the fact that the effective statistical interaction is a traceless operator.     

The non-abelian self-dual string

Letters in Mathematical Physics - We argue that the relevant higher gauge group for the non-abelian generalization of the self-dual string equation is the string 2-group. We then derive the...     

Symmetry groups and non-abelian cohomology

We consider the implementation of symmetry groups of automorphisms of an algebra of observables in a reducible representation whose multipliers in general are non-commuting operators in the commutant of the representation. The multipliers obey a non-abelian cocycle relation which generalizes the 2-cohomology of the group. Examples are given from the theory of spin algebras and continuous tensor products. For typeI representations we show that the multiplier can be chosen to lie in the centre, giving an isomorphism with abelian theory.Dedicated to Res Jost and Arthur Wightman     

The Relativistic non-abelian Chern-Simons Equations

We study ther xr system of nonlinear elliptic equations ,a=1,2,...,r,x∈R ², where λ τ 0 is a constant parameter,K = (K_ab) is the Cartan matrix of a semi-simple Lie algebra, and β_p is the Dirac measure concentrated atp R ². This system of equations arises in the relativistic non-Abelian Chern-Simons theory and may be viewed as a nonintegrable deformation of the integrable Toda system. We establish the existence of a class of solutions known as topological multivortices. The crucial step in our method is the use of the decomposition theorem of Cholesky for positive definite matrices so that a variational principle can be formulated. Research supported in part by the National Science Foundation under grant DMS-9596041     

Actions for non-abelian twisted self-duality

The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective field strengths are dual to each other. It is well known that such equations can be integrated to a local action that carries on equal footing the p-forms together with their duals and is manifestly duality invariant. Space-time covariance is no longer manifest but still present with a non-standard realization of space-time diffeomorphisms on the gauge fields. In this paper, we give a non-abelian generalization of this first-order action by gauging part of its global symmetries. The resulting field equations are non-abelian versions of the twisted self-duality equations. A key element in the construction is the introduction of proper couplings to higher-rank tensor fields. We discuss possible applications (to Yang-Mills and supergravity theories) and comment on the relation to previous no-go theorems.     

Composite optical vortices in noncollinear Laguerre--Gaussian beams and their propagation in free space

Taking two Laguerre-Gaussian beams with topological charge 1 = ±1 as an example, this paper studies the composite optical vortices formed by two noncollinear Laguerre-Gaussian beams with different phases, amplitudes, waist widths, off-axis distances, and their propagation in free space. It is shown by detailed numerical illustrative examples that the number and location of composite vortices at the waist plane are variable by varying the relative phase β, amplitude ratio η, waist width ratio ξ, or off-axis distance ratio μ. The net topological charge lnet is not always equal to the sum lsum of charges of the two component beams. The motion, creation and annihilation of composite vortices take place in the free-space propagation, and the net charge during the propagation remains unchanged and equals to the net charge at the waist plane.     

Vector Bundle Moduli

We give the general presciption for calculating the number of moduli of irreducible, stable U(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. Vector bundle moduli appear as gauge singlet scalar fields in the effective low-energy actions of heterotic superstrings and heterotic M-theory.