Universal reconnection of non-Abelian cosmic strings

We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings.     

Interactions of strings and D-branes from M theory

We discuss the relation between M theory and type II string theories. We show that, assuming “natural” interactions between membranes and fivebranes in M theory, the known interactions between strings and D-branes in type II string theories arise in appropriate limits. Our discussion of the interactions is purely at the classical level. We remark on issues associated with the M theory approach to enhanced gauge symmetries, which deserve further investigation.     

Non-Abelian global strings at chiral phase transition

We construct non-Abelian global string solutions in the UL_(N)×UR_(N)$U{(N)}_{\mathrm{L}}\times U{(N)}_{\mathrm{R}}$ linear sigma model. These strings are the most fundamental objects which are expected to form during the chiral phase transitions, because the Abelian η^′${\eta }^{\prime }$ string is marginally decomposed into N   of them. We point out Nambu–Goldstone modes of CPN−1$\mathbf{C}{P}^{N-1}$ for breaking of SUV_(N)$\mathit{SU}{(N)}_{\mathrm{V}}$ arise around a non-Abelian vortex.     

On the evolution of global strings in the early universe

We find that a bent global string straightens itself out by dissipation into Nambu-Goldstone (NG) bosons in the order of one oscillation time and that the spectrum of radiated NG bosons is 1/k. In the early universe, the assumption that there is one global string per causal horizon is justified after an initial period during which the effect of the primordial plasma on the motion of the strings is non-negligible. We find that the upper bound that axion radiation by strings places on the axion decay constant is comparable to, but not more stringent than the one derived from coherent oscillations of the axion field, i.e. ∫_a ≲ 10¹²GeV. We also discuss the model-dependence of this bound.     

Interferometry of non-Abelian anyons

We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach-Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they are distinguishable via monodromy with the probe anyons, which also determines the rate of collapse. We give estimates on the number of probes needed to obtain a desired confidence level for the measurement outcome distinguishing between charges, and explicitly work out a number of examples for some significant anyon models. We apply the same techniques to describe interferometry measurements in a double point-contact interferometer realized in fractional quantum Hall systems. To lowest order in tunneling, these results essentially match those from the Mach-Zehnder interferometer, but we also provide the corrections due to processes involving multiple tunnelings. Finally, we give explicit predictions describing state measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore-Read state at ν=5/2 and Read-Rezayi state at ν=12/5.     

Smooth non-Abelian bosonization

We present an extension of “smooth bosonization” to the non-Abelian case. We construct an enlarged theory containing both bosonic and fermionic fields which exhibits a local chiral gauge symmetry. A gauge fixing function depending on one real parameter allows us to interpolate smoothly between a purely fermionic and a purely bosonic representation. The procedure is, in the special case of bosonization, complementary to the approach based on duality.     

Interactions of resonances and global bifurcations in Rayleigh-Benard convection

We present detailed two-parameter experimental studies of hysteresis and overlapping of resonances and secondary Hopf bifurcations in the quasiperiodic regime of low-aspect-ratio Rayleigh-Benard convection in solutions of ³He in superfluid ⁴He. The global bifurcations inferred from this experiment are similar to those observed in numerical studies of two-parameter families of maps of the plane with nonconstant jacobian.     

The non-Abelian bosonic quantum ring

We investigate the dynamics of a spinor Bose-Einstein condensate which is governed by an optically induced non-Abelian gauge potential. Using a ring shaped trap to confine the atoms and a hydrodynamic ansatz, nonlinear Josephson type equations are found to describe the system. The degenerate eigenstates which show rotation are solved exactly. We consider a homogenous filled ring and observe population dynamics between the two quasi-spin components but also space dependent Josephson oscillations. Stable mass currents can be observed which are induced by the constant non-Abelian effective magnetic field in the limit of weak interactions. For strong interactions the appearance of two-component dark soliton-like objects are observed.     

Entanglement spectrum of non-Abelian anyons

Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore—Read fractional quantum Hall state. Its quasihole states are zero-energy eigenstates of a parent Hamiltonian, but its quasiparticle states are not. Both of them can be modeled on an equal footing using the bipartite composite fermion method. We study the entanglement spectrum of the cases with two or four non-Abelian anyons. The counting of levels in the entanglement spectrum can be understood using the edge theory of the Moore—Read state, which reflects the topological order of the system. It is shown that the fusion results of two non-Abelian anyons is determined by their distributions in the bipartite construction.     

Charge conjugation of non-Abelian gauge fields

Questions associated with the determination of the charge conjugation in non-Abelian gauge fields are investigated. It is shown that the properties of gauge groups allow the charge conjugation to be simply determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 62–64, April, 1982.     

Super-symmetry and non-Abelian gauges

We show that the conventional Yang-Mills Lagrangian with the Yang-Mills field interacting with Majorana fermions belonging to the adjoint representation of an internal symmetry group like SU(n) is super-gauge invariant.     

On non-Abelian Thomas-Fermi screening

The Thomas-Fermi screening of non-Abelian gauge fields by fermions or screening of gluon fields in quark matter is discussed. It is described by an effective mass term which is, as with hard thermal loops, related to the eikonal for a Chern-Simons theory and the Wess-Zumino-Witten action.     

Monopole vacuum in non-Abelian theories

It is shown that, in the theory of interacting Yang-Mills fields and a Higgs field, there is a topological degeneracy of Bogomol'nyi-Prasad-Sommerfield (BPS) monopoles and that there arises, in this case, a chromoelectric monopole characterized by a new topological variable that describes transitions between topological states of the monopole in Minkowski space (in just the same way as an instanton describes such transitions in Euclidean space). The limit of an infinitely large mass of the Higgs field at a finite density of the Bogomol'nyi-Prasad-Sommerfield monopole is considered as a model of the stable vacuum in pure Yang-Mills theory. It is shown that, in QCD, such a monopole vacuum may lead to a growing potential, a topological confinement, and an additional mass of the η₀ meson. The relationship between the result obtained here for the generating functional of perturbation theory and the Faddeev-Popov integral is discussed.