Transgression of D-branes

Closed strings can be seen either as one-dimensional objects in a target space or as points in the free loop space. Correspondingly, a B-field can be seen either as a connection on a gerbe over the target space, or as a connection on a line bundle over the loop space. Transgression establishes an equivalence between these two perspectives. Open strings require D-branes: submanifolds equipped with vector bundles twisted by the gerbe. In this paper we develop a loop space perspective on D-branes. It involves bundles of simple Frobenius algebras over the branes, together with bundles of bimodules over spaces of paths connecting two branes. We prove that the classical and our new perspectives on D-branes are equivalent. Further, we compare our loop space perspective to Moore-Segal/Lauda-Pfeiffer data for open-closed 2-dimensional topological quantum field theories, and exhibit it as a smooth family of reflection-positive, colored knowledgable Frobenius algebras

A method of deforming G-structures

We consider deformations of G-structures via the right action on the frame bundle in a base-point-dependent manner. We investigate which of these deformations again lead to G-structures and in which cases the original and the deformed G-structures define the same instantons. Further, we construct a bijection from connections compatible with the original G-structure to those compatible with the deformed G-structure and investigate the change of intrinsic torsion under the aforementioned deformations. Finally, we consider several examples.Comment: 14 pages; v3: references added, published in Journal of Geometry and Physic

Study of a new simulation algorithm for dynamical quarks on the APE-100 parallel computer

First results on the autocorrelation behaviour of a recently proposed fermion algorithm by M. L\"uscher are presented and discussed. The occurence of unexpected large autocorrelation times is explained. Possible improvements are discussed.Comment: 3 pages, compressed ps-file (uufiles), Contribution to Lattice 9

A Perturbative RS I Cosmological Phase Transition

We identify a class of Randall-Sundrum type models with a successful first order cosmological phase transition during which a 5D dual of approximate conformal symmetry is spontaneously broken. Our focus is on soft-wall models that naturally realize a light radion/dilaton and suppressed dynamical contribution to the cosmological constant. We discuss phenomenology of the phase transition after developing a theoretical and numerical analysis of these models both at zero and finite temperature. We demonstrate a model with a TeV-Planck hierarchy and with a successful cosmological phase transition where the UV value of the curvature corresponds, via AdS/CFT, to an $N$ of $20$, where 5D gravity is expected to be firmly in the perturbative regime.Comment: 34pp, 12 figure

Computing the lowest eigenvalues of the Fermion matrix by subspace iterations

Subspace iterations are used to minimise a generalised Ritz functional of a large, sparse Hermitean matrix. In this way, the lowest $m$ eigenvalues are determined. Tests with $1 \leq m \leq 32$ demonstrate that the computational cost (no. of matrix multiplies) does not increase substantially with $m$. This implies that, as compared to the case of a $m=1$, the additional eigenvalues are obtained for free.Comment: Talk presented at LATTICE96(algorithms), 3 pages, 2 Postscript figures, uses epsf.sty, espcrc2.st

Fractional Inversion in Krylov Space

The fractional inverse $M^{-\gamma}$ (real $\gamma >0$) of a matrix $M$ is expanded in a series of Gegenbauer polynomials. If the spectrum of $M$ is confined to an ellipse not including the origin, convergence is exponential, with the same rate as for Chebyshev inversion. The approximants can be improved recursively and lead to an iterative solver for $M^\gamma x = b$ in Krylov space. In case of $\gamma = 1/2$, the expansion is in terms of Legendre polynomials, and rigorous bounds for the truncation error are derived.Comment: Contribution to LAT97 proceedings, 3 page

The 2-Hilbert Space of a Prequantum Bundle Gerbe

We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier-Douady class is torsion. Analogously to usual prequantisation, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf's version of the 2-category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbes and turns the category of sections into a 2-Hilbert space. We discuss how these 2-Hilbert spaces fit various expectations from higher prequantisation. We then extend the transgression functor to the full 2-category of bundle gerbes and demonstrate its compatibility with the additional structures introduced. We discuss various aspects of Kostant-Souriau prequantisation in this setting, including its dimensional reduction to ordinary prequantisation.Comment: 97 pages; v2: minor changes; Final version to be published in Reviews in Mathematical Physic

Two-flavour Schwinger model with dynamical fermions in the L\"uscher formalism

We report preliminary results for 2D massive QED with two flavours of Wilson fermions, using the Hermitean variant of L\"uscher's bosonization technique. The chiral condensate and meson masses are obtained. The simplicity of the model allows for high statistics simulations close to the chiral and continuum limit, both in the quenched approximation and with dynamical fermions.Comment: Talk presented at LATTICE96(algorithms), 3 pages, 3 Postscript figures, uses twoside, fleqn, espcrc2, epsf, revised version (details of approx. polynomial

Finite Temperature Reduction of the SU(2) Higgs-Model with Complete Static Background

Direct evaluation of the 1-loop fluctuation determinant of non-static degrees of freedom in a complete static background is advocated to be more efficient for the determination of the effective three-dimensional model of the electroweak phase transition than the one-by-one evaluation of Feynman diagrams. The relation of the couplings and fields of the effective model to those of the four-dimensional finite temperature system is determined in the general 't Hooft gauge with full implementation of renormalisation effects. Only field renormalisation constants display dependence on the gauge fixing parameter. Characteristics of the electroweak transition are computed from the effective theory in Lorentz-gauge. The dependence of various physical observables on the three-dimensional gauge fixing parameter is investigated.Comment: 12 pages (LATEX) + 1 table (TEX) appende