56 research outputs found
Charges of Exceptionally Twisted Branes
The charges of the exceptionally twisted (D4 with triality and E6 with charge
conjugation) D-branes of WZW models are determined from the microscopic/CFT
point of view. The branes are labeled by twisted representations of the affine
algebra, and their charge is determined to be the ground state multiplicity of
the twisted representation. It is explicitly shown using Lie theory that the
charge groups of these twisted branes are the same as those of the untwisted
ones, confirming the macroscopic K-theoretic calculation. A key ingredient in
our proof is that, surprisingly, the G2 and F4 Weyl dimensions see the simple
currents of A2 and D4, respectively.Comment: 19 pages, 2 figures, LaTex2e, complete proofs of all statements,
updated bibliograph
Twisted brane charges for non-simply connected groups
The charges of the twisted branes for strings on the group manifold SU(n)/Z_d
are determined. To this end we derive explicit (and remarkably simple) formulae
for the relevant NIM-rep coefficients. The charge groups of the twisted and
untwisted branes are compared and found to agree for the cases we consider.Comment: 30 page
Charges of twisted branes: the exceptional cases
The charges of the twisted D-branes for the two exceptional cases (SO(8) with
the triality automorphism and E_6 with charge conjugation) are determined. To
this end the corresponding NIM-reps are expressed in terms of the fusion rules
of the invariant subalgebras. As expected the charge groups are found to agree
with those characterising the untwisted branes.Comment: 15 page
D-brane charges on non-simply connected groups
The maximally symmetric D-branes of string theory on the non-simply connected
Lie group SU(n)/Z_d are analysed using conformal field theory methods, and
their charges are determined. Unlike the well understood case for simply
connected groups, the charge equations do not determine the charges uniquely,
and the charge group associated to these D-branes is therefore in general not
cyclic. The precise structure of the charge group depends on some number
theoretic properties of n, d, and the level of the underlying affine algebra k.
The examples of SO(3)=SU(2)/Z_2 and SU(3)/Z_3 are worked out in detail, and the
charge groups for SU(n)/Z_d at most levels k are determined explicitly.Comment: 31 pages, 1 figure. 2 refs added. Added the observation: the charge
group for each su(2) theory equals the centre of corresponding A-D-E grou
On the complete classification of the unitary N=2 minimal superconformal field theories
Aiming at a complete classification of unitary N=2 minimal models (where the
assumption of space-time supersymmetry has been dropped), it is shown that each
modular invariant candidate of a partition function for such a theory is indeed
the partition function of a minimal model. A family of models constructed via
orbifoldings of either the diagonal model or of the space-time supersymmetric
exceptional models demonstrates that there exists a unitary N=2 minimal model
for every one of the allowed partition functions in the list obtained from
Gannon's work.
Kreuzer and Schellekens' conjecture that all simple current invariants can be
obtained as orbifolds of the diagonal model, even when the extra assumption of
higher-genus modular invariance is dropped, is confirmed in the case of the
unitary N=2 minimal models by simple counting arguments.Comment: 53 pages; Latex; minor changes in v2: intro expanded, references
added, typos corrected, footnote added on p31; renumbering of sections; main
theorem reformulated for clarity, but contents unchanged. Minor revisions in
v3: typos corrected, footnotes 5, 6 added, lemma 1 and section 3.3.2
rewritten for greater generality, section 3.3 review removed. To appear in
Comm. Math. Phy
Branes in the plane wave background with gauge field condensates
Supersymmetric branes in the plane wave background with additional constant
magnetic fields are studied from the world-sheet point of view. It is found
that in contradistinction to flat space, boundary condensates on some maximally
supersymmetric branes necessarily break at least some supersymmetries. The
maximally supersymmetric cases with condensates are shown to be in one to one
correspondence with the previously classified class II branes.Comment: LaTeX, 31 pages, no figures; v2: references added, some typos
correcte
Loop Operators and the Kondo Problem
We analyse the renormalisation group flow for D-branes in WZW models from the
point of view of the boundary states. To this end we consider loop operators
that perturb the boundary states away from their ultraviolet fixed points, and
show how to regularise and renormalise them consistently with the global
symmetries of the problem. We pay particular attention to the chiral operators
that only depend on left-moving currents, and which are attractors of the
renormalisation group flow. We check (to lowest non-trivial order in the
coupling constant) that at their stable infrared fixed points these operators
measure quantum monodromies, in agreement with previous semiclassical studies.
Our results help clarify the general relationship between boundary transfer
matrices and defect lines, which parallels the relation between
(non-commutative) fields on (a stack of) D-branes and their push-forwards to
the target-space bulk.Comment: 22 pages, 2 figure
Modular Invariants in the Fractional Quantum Hall Effect
We investigate the modular properties of the characters which appear in the
partition functions of nonabelian fractional quantum Hall states. We first give
the annulus partition function for nonabelian FQH states formed by spinon and
holon (spinon-holon state). The degrees of freedom of spin are described by the
affine SU(2) Kac-Moody algebra at level . The partition function and the
Hilbert space of the edge excitations decomposed differently according to
whether is even or odd. We then investigate the full modular properties of
the extended characters for nonabelian fractional quantum Hall states. We
explicitly verify the modular invariance of the annulus grand partition
functions for spinon-holon states, the Pfaffian state and the 331 states. This
enables one to extend the relation between the modular behavior and the
topological order to nonabelian cases. For the Haldane-Rezayi state, we find
that the extended characters do not form a representation of the modular group,
thus the modular invariance is broken.Comment: Latex,21 pages.version to appear in Nucl.Phys.
G(2) quivers
We present, in explicit matrix representation and a modernity befitting the community, the classification of the finite discrete subgroups of G2 and compute the McKay quivers arising therefrom. Of physical interest are the classes of Script N = 1 gauge theories descending from M-theory and of mathematical interest are possible steps toward a systematic study of crepant resolutions to smooth G2 manifolds as well as generalised McKay Correspondences. This writing is a companion monograph to hep-th/9811183 and hep-th/9905212, wherein the analogues for Calabi-Yau three- and four-folds were considered
Lectures on conformal field theory and Kac-Moody algebras
This is an introduction to the basic ideas and to a few further selected
topics in conformal quantum field theory and in the theory of Kac-Moody
algebras.Comment: 59 pages, LaTeX2e, extended version of lectures given at the Graduate
Course on Conformal Field Theory and Integrable Models (Budapest, August
1996), to appear in Springer Lecture Notes in Physic
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