Higgs Fields,Bundle Gerbes and String Structures

We use bundle gerbes and their connections and curvings to obtain an explicit formula for a de Rham representative of the string class of a loop group bundle. This is related to earlier work on calorons.Both authors acknowledge the support of the Australian Research Council.     

Geodesics on loop spaces

The space of loops smoothly embedded into a Riemannian manifold, being a principal fibre bundle with structure group Diff S¹, is investigated from a Kaluza-Klein type point of view. In particular, the Levi-Civita connection for the natural Diff S¹-invariant metric on this loop space is calculated and the corresponding horizontal geodesics (the analogue of classical free motion of point particles) are characterized. Finally, an explicit solution is given in the case of loops in ³.     

String structures on loop bundles

Differential geometry and topology of principal loop bundles (bundles of loop groups over loop spaces) are investigated. String structures, defined as bundle extensions corresponding to the central extension of the structure group, do not always exist. Various methods for deriving the obstruction to the existence of string structures are discussed.Supported in part by the U.S. Department of Energy under Grant #DE-FG02-84ER40158 with Harvard University.Supported in part by the NSF Grant #87-08447 and by the U.S. Department of Energy under Contract #DE-AC02-76ER-03069.On leave from the University of Wroclaw, Wroclaw, Poland     

Charged string loops in Reissner–Nordström black hole background

We study the motion of current carrying charged string loops in the Reissner–Nordström black hole background combining the gravitational and electromagnetic field. Introducing new electromagnetic interaction between central charge and charged string loop makes the string loop equations of motion to be non-integrable even in the flat spacetime limit, but it can be governed by an effective potential even in the black hole background. We classify different types of the string loop trajectories using effective potential approach, and we compare the innermost stable string loop positions with loci of the charged particle innermost stable orbits. We examine string loop small oscillations around minima of the string loop effective potential, and we plot radial profiles of the string loop oscillation frequencies for both the radial and vertical modes. We construct charged string loop quasi-periodic oscillations model and we compare it with observed data from microquasars GRO 1655-40, XTE 1550-564, and GRS 1915+105. We also study the acceleration of current carrying string loops along the vertical axis and the string loop ejection from RN black hole neighbourhood, taking also into account the electromagnetic interaction.     

Radiation from cosmic chiral string loops

The gravitational and electromagnetic radiation from chiral superconducting cosmic string loops is calculated. The formulas for energy, momentum, and angular momentum losses due to gravitational and electromagnetic radiation from chiral loops of an arbitrary configuration are derived. After summation over all modes, expressions for the corresponding radiation rates averaged over the loop oscillation period have the form of four-dimensional integrals. These formulas are reduced to sums over the kinks for loops composed of piece-wise linear strings. For three examples of string loops, the total radiation rates are calculated numerically depending on the chiral current along the string. In the limit of a nearly maximum current, which corresponds to a stationary loop (vorton) configuration, we determine the upper bounds on the gravitational and electromagnetic radiation. We also estimate the oscillation damping time of a nearly stationary loop.     

Principal Bundles and the Dixmier Douady Class

A systematic consideration of the problem of the reduction and “lifting” of the structure group of a principal bundle is made and a variety of techniques in each case are explored and related to one another. We apply these to the study of the Dixmier-Douady class in various contexts including string structures, bundles and other examples motivated by considerations from quantum field theory. Received: 26 February 1997 / Accepted: 5 August 1997     

Non-parametric strings

A formulation to relate the free bosonic string to the geometry of the group of loops is discussed. A neat implementation of the quantum dynamics and the constraints is found in terms of contact loop deformations.     

The Importance of Quantum Effects in Superconducting Cosmic Strings

Classical current-carrying cosmic string loopmotion is investigated by means of a numericalsimulation making explicit use of the Carter formalismand the Carter-Peter rational and logarithmic equations of state. The class of initial configurationsconsists of elliptic loops far from the vortonequilibrium state with constant state parameter alongthe loop. Thus, the relevant parameters, apart fromthose describing the equation of state itself, arethe ellipticity and the initial state parameter. It isfound that for most of the parameter space, the loopmotion is quasiperiodic, but that this result is actually irrelevant to the treatment of anarbitrary loop motion: indeed, almost systematically,the loops develop kinks and cusps, and in the case ofspacelike currents, there are segments of the loop that escape the elastic regime. It is thenargued that quantum effects resulting from thesesituations will in practice provide the dominantevolution mechanisms.     

The conformal factor and DiffS1/S1

Two-dimensional gravity coupled with an open string is considered to geometrically construct a string field theory following Bowick and Rajeev. The phase space of this system can be thought of as an extended loop space, and is in fact a Kähler manifold. Each loop carries a conformal factor. Bowick and Rajeev's proposal is modified so that the ghost fields stand on the same footing as the x^μ-fields. The closed string field is modified to be the Kähler potential of the extended loop space. The canonical line bundle is not needed for the equation of motion for a closed string field. A covariant (free) open string field theory is constructed as a by-product in this approach.     

Low frequency gravity wave spectra generated by cosmic strings

Gravity wave spectra generated by populations of cosmic string loops are computed, showing that loop evolution and radiation properties have important effects at observable wavelengths. The spectra are compared with limits derived from various observations; bounds from millisecond pulsar timing are becoming severe for several string scenarios, but implied constraints on string parameters depend sensitively on details of the loop population and dynamics.     

The Circular Loop Equation of a Cosmic String with Time-Varying Tension in de Sitter Spacetimes

In this work the equation of circular loops of cosmic string possessing time-dependent tension is studied in the de Sitter spacetime. We find that the cosmic string loops with initial radius r(t ₀)>0.707L, L de Sitter radius, should not collapse to form a black hole. It is also found that in the case of r(t ₀)<0.707L a loop of cosmic string whose tension depends on some power of cosmic time can not become a black hole if the power is lower than a critical value which is associated with the initial size of the loop. Our research gives rise to some important corrections to the conclusion in the case of loops of cosmic string with constant tension in the same background.     

Reconstruction theorem for groupoids and principal fiber bundles

The loop space formulation of 3+1 canonical quantum gravity premises that all physical information is contained within the holonomy loop functionals. This assumption is the result of the reconstruction theorem for a principla fiber bundle on a base loop space. The gauge connection for interacting gauge theories is more appropriately and readily reconstructed on a path space as opposed to a loop space. We generalize the reconstruction theorem to a base path space. Employing a holonomy groupoid map and a path connection, we trivially construct an abstract Lie groupoid from which a principal fiber bundle and gauge connection can be derived as distinctive examples. The groupoid reconstruction theorem is valid on both connected and nonconnected base manifolds, unlike the holonomy group reconstruction theorem, which can only be utilized for connected manifolds.     

Flux-tube formation and holographic tunneling

We consider correlator of two concentric Wilson loops, a small and large ones related to the problem of flux-tube formation. There are three mechanisms which can contribute to the connected correlator and yield different dependences on the radius of the small loop. The first one is quite standard and concerns exchange by supergravity modes. We also consider a novel mechanism when the flux-tube formation is described by a barrier transition in the string language, dual to the field-theoretic formulation of Yang–Mills theories. The most interesting possibility within this approach is resonant tunneling which would enhance the correlator of the Wilson loops for particular geometries. The third possibility involves exchange by a dyonic string supplied with the string junction. We introduce also 't Hooft and composite dyonic loops as probes of the flux tube. Implications for lattice measurements are briefly discussed.     

Another construction of the central extension of the loop group

By considering the geometry of the central extension of the loop group as a principal bundle it is shown that it must be the quotient of a larger group. This group is a central extension of the group of paths in the loop group and its cocycle is constructed as the holonomy around a certain path. Conversely it is shown that this definition of a cocycle gives a method of constructing the central extension. The Wess-Zumino term plays an important role in these constructions.     

The stability of cosmic string loops

A general perturbation analysis is performed on closed string loops to investigate whether small perturbations cause the known class of non-self-intersecting loops to self-intersect. This leads to the conclusion that most of this class of loops are stable to small perturbations.     

Analytic approach to confinement and monopoles in lattice SU (2)

We extend the approach of Banks, Myerson, and Kogut for the calculation of the Wilson loop in lattice U (1) to the non-abelian SU (2) group. The original degrees of freedom of the theory are integrated out, new degrees of freedom are introduced in several steps. The centre group enters automatically through the appearance of a field strength tensor , which takes on the values 0 or 1 only. It obeys a linear field equation with the loop current as source. This equation implies that is non vanishing on a two-dimensional surface bounded by the loop, and possibly on closed surfaces. The two-dimensional surfaces have a natural interpretation as strings moving in euclidean time. In four dimensions we recover the dual Abrikosov string of a type II superconductor, i.e. an electric string encircled by a magnetic current. In contrast to other types of monopoles found in the literature, the monopoles and the associated magnetic currents are present in every configuration. With some plausible, though not generally conclusive, arguments we are directly led to the area law for large loops. Received: 27 August 1999 / Revised version: 29 October 1999 / Published online: 21 December 1999     

Fusion of Symmetric D-Branes and Verlinde Rings

We explain how multiplicative bundle gerbes over a compact, connected and simple Lie group G lead to a certain fusion category of equivariant bundle gerbe modules given by pre-quantizable Hamiltonian LG-manifolds arising from Alekseev-Malkin-Meinrenken’s quasi-Hamiltonian G-spaces. The motivation comes from string theory namely, by generalising the notion of D-branes in G to allow subsets of G that are the image of a G-valued moment map we can define a ‘fusion of D-branes’ and a map to the Verlinde ring of the loop group of G which preserves the product structure. The idea is suggested by the theorem of Freed-Hopkins-Teleman. The case where G is not simply connected is studied carefully in terms of equivariant bundle gerbe modules for multiplicative bundle gerbes.     

Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds

We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(3) holonomy then the equations of motion derived from the heterotic string effective action are also satisfied by the solutions we obtain.