178 research outputs found
D-branes in group manifolds and flux stabilization
We consider D-branes in group manifolds, from the point of view of open
strings and using the Born-Infeld action on the brane worldvolume. D-branes
correspond to certain integral (twined) conjugacy classes. We explain the
integrality condition on the conjugacy classes in both approaches. In the
Born-Infeld description, the D-brane worldvolume is stabilized against
shrinking by a subtle interplay of quantized U(1) fluxes and the non-triviality
of the B-field.Comment: 6 pages. Invited talk at the 9th Marcel Grossmann meeting, Rome, July
200
Equivariance In Higher Geometry
We study (pre-)sheaves in bicategories on geometric categories: smooth
manifolds, manifolds with a Lie group action and Lie groupoids. We present
three main results: we describe equivariant descent, we generalize the plus
construction to our setting and show that the plus construction yields a
2-stackification for 2-prestacks. Finally we show that, for a 2-stack, the
pullback functor along a Morita-equivalence of Lie groupoids is an equivalence
of bicategories. Our results have direct applications to gerbes and 2-vector
bundles. For instance, they allow to construct equivariant gerbes from local
data and can be used to simplify the description of the local data. We
illustrate the usefulness of our results in a systematic discussion of
holonomies for unoriented surfaces.Comment: 42 pages, minor correction
Hopf algebras and finite tensor categories in conformal field theory
In conformal field theory the understanding of correlation functions can be
divided into two distinct conceptual levels: The analytic properties of the
correlators endow the representation categories of the underlying chiral
symmetry algebras with additional structure, which in suitable cases is the one
of a finite tensor category. The problem of specifying the correlators can then
be encoded in algebraic structure internal to those categories. After reviewing
results for conformal field theories for which these representation categories
are semisimple, we explain what is known about representation categories of
chiral symmetry algebras that are not semisimple. We focus on generalizations
of the Verlinde formula, for which certain finite-dimensional complex Hopf
algebras are used as a tool, and on the structural importance of the presence
of a Hopf algebra internal to finite tensor categories.Comment: 46 pages, several figures. v2: missing text added after (4.5),
references added, and a few minor changes. v3: typos corrected, bibliography
update
Modular categories from finite crossed modules
It is known that finite crossed modules provide premodular tensor categories.
These categories are in fact modularizable. We construct the modularization and
show that it is equivalent to the module category of a finite Drinfeld double.Comment: 21 pages, typos correcte
A note on permutation twist defects in topological bilayer phases
We present a mathematical derivation of some of the most important physical
quantities arising in topological bilayer systems with permutation twist
defects as introduced by Barkeshli et al. in cond-mat/1208.4834. A crucial tool
is the theory of permutation equivariant modular functors developed by Barmeier
et al. in math.CT/0812.0986 and math.QA/1004.1825.Comment: 18 pages, some figure
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