46 research outputs found
A note on D-branes in group manifolds: flux quantisation and D0-charge
We show that a D-brane in a group manifold given by a (twisted) conjugacy
class is characterised by a gauge invariant two-form field determined in terms
of the matrix of gluing conditions. Using a quantisation argument based on the
path integral one obtains the known quantisation condition for the
corresponding D-branes. We find no evidence for the existence of a quantised
U(1) gauge field flux. We propose an expression for the D0 charge of such
D-branes.Comment: 13 pages. (v2: minor changes, some comments and references added.
D-branes in curved spacetime: Nappi-Witten background
We find exact D-brane configurations in the Nappi-Witten background using the
boundary state approach and describe how they are related by T-duality
transformations. We also show that the classical boundary conditions of the
associated sigma model correspond to a field dependent automorphism relating
the chiral currents and discuss the correspondence between the boundary state
approach and the sigma model approach.Comment: 21 pages, 7 figures, references adde
The energy operator for infinite statistics
We construct the energy operator for particles obeying infinite statistics
defined by a q-deformation of the Heisenberg algebra.
(This paper appeared published in CMP in 1992, but was not archived at the
time.)Comment: 6 page
Supersymmetric Integrable Hierarchies and String Theory
This thesis is roughly organized into two parts. The first one (the first
three chapters), expository in nature, attempts to place the current work in
context: at first historically, but then focusing on the Lax formalism and the
Adler--Gel'fand--Dickey scheme for hierarchies of the KdV type. The second part
(the last four chapters) comprises the main body of this work. It begins by
developing the supersymmetric Lax formalism, introducing the ring of formal
superpseudodifferential operators and the associated Poisson structures. We
discuss three supersymmetric extensions of the KP hierarchy (MRSKP, \SKP2, and
JSKP). We define and compute their additional symmetries and we find that the
algebra of additional symmetries are in all three cases isomorphic to the Lie
algebra of superdifferential operators. We discuss a new reduction of \SKP2 and
the relation between MRSKP and \SKP2 is clarified. Finally we consider the (so
far) only integrable hierarchy to have played a role in noncritical superstring
theory (sKdV-B). We identify it, prove its bihamiltonian integrability, and
extend it by odd flows. We close with a discussion of new integrable
supersymmetrizations of the KdV-like hierarchies suggested by the study of
sKdV-B. (This is the author's PhD Thesis from the Physics Deparment of the
University of Bonn, July 1994.)Comment: 118 pages, uuencoded compressed .dvi files + 4 figures. Requires
epsf.tex and the AMSFonts (v. 2.1+), BONN-IR-94-0
On the structure of symmetric self-dual Lie algebras
A finite-dimensional Lie algebra is called (symmetric) self-dual, if it
possesses an invariant nondegenerate (symmetric) bilinear form. Symmetric
self-dual Lie algebras have been studied by Medina and Revoy, who have proven a
very useful theorem about their structure. In this paper we prove a refinement
of their theorem which has wide applicability in Conformal Field Theory, where
symmetric self-dual Lie algebras start to play an important role due to the
fact that they are precisely the Lie algebras which admit a Sugawara
construction. We also prove a few corollaries which are important in Conformal
Field Theory. (This paper provides mathematical details of results used, but
only sketched, in the companion paper hep-th/9506151.)Comment: 19 pages, .dvi.uu (needs AMSFonts 2.1+
Nonsemisimple Sugawara Constructions
By a Sugawara construction we mean a generalized Virasoro construction in
which the currents are primary fields of conformal weight one. For simple Lie
algebras, this singles out the standard Sugawara construction out of all the
solutions to the Virasoro master equation. Examples of nonsemisimple Sugawara
constructions have appeared recently. They share the properties that the
Virasoro central charge is an integer equal to the dimension of the Lie algebra
and that they can be obtained by high-level contraction of reductive Sugawara
constructions: they thus correspond to free bosons. Exploiting a recent
structure theorem for Lie algebras with an invariant metric, we are able to
unify all the known constructions under the same formalism and, at the same
time, to prove several results about the Sugawara constructions. In particular,
we prove that all such constructions factorize into a standard (semisimple)
Sugawara construction and a nonsemisimple one (with integral central charge) of
a form which generalizes the nonsemisimple examples known so far.Comment: uuencoded compressed .dvi file (needs AMSFonts 2.1+), 13 document
pages but 7 physical page
Gauged Wess-Zumino terms and Equivariant Cohomology
We summarize some results obtained on the problem of gauging the Wess--Zumino
term of a d-dimensional bosonic sigma-model. We show that gauged WZ-like terms
are in one-to-one correspondence with equivariant cocycles of the target space.
By the same token, the obstructions to gauging a WZ term can be understood in
terms of the equivariant cohomology of the target space and this allows us to
use topological tools to derive some a priori vanishing theorems guaranteeing
the absence of obstructions for a large class of target spaces and symmetry
groups in the physically interesting dimensions d<=4. (This is an expository
summary of the results of hep-th/9407149.)Comment: 11 pages, uuencoded compressed .dvi file (uses AMSFonts 2.1+),
QMW-PH-94-2