779 research outputs found
Branching rules of semi-simple Lie algebras using affine extensions
We present a closed formula for the branching coefficients of an embedding p
in g of two finite-dimensional semi-simple Lie algebras. The formula is based
on the untwisted affine extension of p. It leads to an alternative proof of a
simple algorithm for the computation of branching rules which is an analog of
the Racah-Speiser algorithm for tensor products. We present some simple
applications and describe how integral representations for branching
coefficients can be obtained. In the last part we comment on the relation of
our approach to the theory of NIM-reps of the fusion rings of WZW models with
chiral algebra g_k. In fact, it turns out that for these models each embedding
p in g induces a NIM-rep at level k to infinity. In cases where these NIM-reps
can be be extended to finite level, we obtain a Verlinde-like formula for
branching coefficients.Comment: 11 pages, LaTeX, v2: one reference added, v3: Clarified proof of
Theorem 2, completely rewrote and extended Section 5 (relation to CFT), added
various references. Accepted for publication in J. Phys.
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
About Attitudes and Perceptions: Finding the Proper Way to Consider Latent Variables in Discrete Choice Models
Coulomb-gas formulation of SU(2) branes and chiral blocks
We construct boundary states in WZNW models using the bosonized
Wakimoto free-field representation and study their properties. We introduce a
Fock space representation of Ishibashi states which are coherent states of
bosons with zero-mode momenta (boundary Coulomb-gas charges) summed over
certain lattices according to Fock space resolution of . The Virasoro
invariance of the coherent states leads to families of boundary states
including the B-type D-branes found by Maldacena, Moore and Seiberg, as well as
the A-type corresponding to trivial current gluing conditions. We then use the
Coulomb-gas technique to compute exact correlation functions of WZNW primary
fields on the disk topology with A- and B-type Cardy states on the boundary. We
check that the obtained chiral blocks for A-branes are solutions of the
Knizhnik-Zamolodchikov equations.Comment: 14 pages, 3 figures, revtex4. Essentially the published versio
Conformal Orbifold Partition Functions from Topologically Massive Gauge Theory
We continue the development of the topological membrane approach to open and
unoriented string theories. We study orbifolds of topologically massive gauge
theory defined on the geometry , where is a generic
compact Riemann surface. The orbifold operations are constructed by gauging the
discrete symmetries of the bulk three-dimensional field theory. Multi-loop
bosonic string vacuum amplitudes are thereby computed as bulk correlation
functions of the gauge theory. It is shown that the three-dimensional
correlators naturally reproduce twisted and untwisted sectors in the case of
closed worldsheet orbifolds, and Neumann and Dirichlet boundary conditions in
the case of open ones. The bulk wavefunctions are used to explicitly construct
the characters of the underlying extended Kac-Moody group for arbitrary genus.
The correlators for both the original theory and its orbifolds give the
expected modular invariant statistical sums over the characters.Comment: 47 pages LaTeX, 3 figures, uses amsfonts and epsfig; v2: Typos
corrected, reference added, clarifying comments on modular invariance
inserted; v3: Further comments on modular invariance added; to be published
in JHE
D-branes in T-fold conformal field theory
We investigate boundary dynamics of orbifold conformal field theory involving
T-duality twists. Such models typically appear in contexts of non-geometric
string compactifications that are called monodrofolds or T-folds in recent
literature. We use the framework of boundary conformal field theory to analyse
the models from a microscopic world-sheet perspective. In these backgrounds
there are two kinds of D-branes that are analogous to bulk and fractional
branes in standard orbifold models. The bulk D-branes in T-folds allow
intuitive geometrical interpretations and are consistent with the classical
analysis based on the doubled torus formalism. The fractional branes, on the
other hand, are `non-geometric' at any point in the moduli space and their
geometric counterparts seem to be missing in the doubled torus analysis. We
compute cylinder amplitudes between the bulk and fractional branes, and find
that the lightest modes of the open string spectra show intriguing non-linear
dependence on the moduli (location of the brane or value of the Wilson line),
suggesting that the physics of T-folds, when D-branes are involved, could
deviate from geometric backgrounds even at low energies. We also extend our
analysis to the models with SU(2) WZW fibre at arbitrary levels.Comment: 38 pages, no figure, ams packages. Essentially the published versio
The charges of a twisted brane
The charges of the twisted D-branes of certain WZW models are determined. The
twisted D-branes are labelled by twisted representations of the affine algebra,
and their charge is simply the ground state multiplicity of the twisted
representation. It is shown that the resulting charge group is isomorphic to
the charge group of the untwisted branes, as had been anticipated from a
K-theory calculation. Our arguments rely on a number of non-trivial Lie
theoretic identities.Comment: 27 pages, 1 figure, harvmac (b
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