9,675 research outputs found
Describing codimension two defects
Codimension two defects of the six dimensional theory
have played an important role in the understanding
of dualities for certain SCFTs in four dimensions. These
defects are typically understood by their behaviour under various dimensional
reduction schemes. In their various guises, the defects admit partial
descriptions in terms of singularities of Hitchin systems, Nahm boundary
conditions or Toda operators. Here, a uniform dictionary between these
descriptions is given for a large class of such defects in
.Comment: 74pp, lots of tables detailing order reversing duality; (v2)
Acknowledgement added. Notation simplified, refs added, minor fixes ; (v3)
Minor changes, version accepted in JHEP. I thank the referee for helpful
comments towards improving presentatio
Minimal kernels of Dirac operators along maps
Let be a closed spin manifold and let be a closed manifold. For maps
and Riemannian metrics on and on , we consider
the Dirac operator of the twisted Dirac bundle . To this Dirac operator one can associate an index
in . If is -dimensional, one gets a lower bound for
the dimension of the kernel of out of this index. We investigate
the question whether this lower bound is obtained for generic tupels
A Rigorous Path Integral for Supersymmetric Quantum Mechanics and the Heat Kernel
In a rigorous construction of the path integral for supersymmetric quantum
mechanics on a Riemann manifold, based on B\"ar and Pf\"affle's use of
piecewise geodesic paths, the kernel of the time evolution operator is the heat
kernel for the Laplacian on forms. The path integral is approximated by the
integral of a form on the space of piecewise geodesic paths which is the
pullback by a natural section of Mathai and Quillen's Thom form of a bundle
over this space.
In the case of closed paths, the bundle is the tangent space to the space of
geodesic paths, and the integral of this form passes in the limit to the
supertrace of the heat kernel.Comment: 14 pages, LaTeX, no fig
Non-solvable contractions of semisimple Lie algebras in low dimension
The problem of non-solvable contractions of Lie algebras is analyzed. By
means of a stability theorem, the problem is shown to be deeply related to the
embeddings among semisimple Lie algebras and the resulting branching rules for
representations. With this procedure, we determine all deformations of
indecomposable Lie algebras having a nontrivial Levi decomposition onto
semisimple Lie algebras of dimension , and obtain the non-solvable
contractions of the latter class of algebras.Comment: 21 pages. 2 Tables, 2 figure
Future asymptotic expansions of Bianchi VIII vacuum metrics
Bianchi VIII vacuum solutions to Einstein's equations are causally
geodesically complete to the future, given an appropriate time orientation, and
the objective of this article is to analyze the asymptotic behaviour of
solutions in this time direction. For the Bianchi class A spacetimes, there is
a formulation of the field equations that was presented in an article by
Wainwright and Hsu, and in a previous article we analyzed the asymptotic
behaviour of solutions in these variables. One objective of this paper is to
give an asymptotic expansion for the metric. Furthermore, we relate this
expansion to the topology of the compactified spatial hypersurfaces of
homogeneity. The compactified spatial hypersurfaces have the topology of
Seifert fibred spaces and we prove that in the case of NUT Bianchi VIII
spacetimes, the length of a circle fibre converges to a positive constant but
that in the case of general Bianchi VIII solutions, the length tends to
infinity at a rate we determine.Comment: 50 pages, no figures. Erronous definition of Seifert fibred spaces
correcte
On weakly maximal representations of surface groups
We introduce and study a new class of representations of surface groups into
Lie groups of Hermitian type, called {\em weakly maximal} representations. We
prove that weakly maximal representations are discrete and injective and we
describe the structure of the Zariski closure of their image. Furthermore we
prove that the set of weakly maximal representations is a closed subset of the
representation variety and describe its relation to other geometrically
significant subsets of the representation variety.Comment: In this version the paper has been split in two parts. The part that
has been removed appears now as http://arxiv.org/abs/1601.02232. The current
version of the paper will appear in the Journal of Differential Geometr
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