3,809 research outputs found
The Tensor Track, III
We provide an informal up-to-date review of the tensor track approach to
quantum gravity. In a long introduction we describe in simple terms the
motivations for this approach. Then the many recent advances are summarized,
with emphasis on some points (Gromov-Hausdorff limit, Loop vertex expansion,
Osterwalder-Schrader positivity...) which, while important for the tensor track
program, are not detailed in the usual quantum gravity literature. We list open
questions in the conclusion and provide a rather extended bibliography.Comment: 53 pages, 6 figure
Vertex algebras and 4-manifold invariants
We propose a way of computing 4-manifold invariants, old and new, as chiral
correlation functions in half-twisted 2d theories that
arise from compactification of fivebranes. Such formulation gives a new
interpretation of some known statements about Seiberg-Witten invariants, such
as the basic class condition, and gives a prediction for structural properties
of the multi-monopole invariants and their non-abelian generalizations.Comment: 67 pages, 11 figure
N=2 Topological Yang-Mills Theory on Compact K\"{a}hler Surfaces
We study a topological Yang-Mills theory with fermionic symmetry. Our
formalism is a field theoretical interpretation of the Donaldson polynomial
invariants on compact K\"{a}hler surfaces. We also study an analogous theory on
compact oriented Riemann surfaces and briefly discuss a possible application of
the Witten's non-Abelian localization formula to the problems in the case of
compact K\"{a}hler surfaces.Comment: ESENAT-93-01 & YUMS-93-10, 34pages: [Final Version] to appear in
Comm. Math. Phy
Rudiments of Holography
An elementary introduction to Maldacena's AdS/CFT correspondence is given,
with some emphasis in the Fefferman-Graham construction. This is based on
lectures given by one of us (E.A.) at the Universidad Autonoma de Madrid.Comment: 60 pages, additional misprints corrected, references adde
Discrete Lie Advection of Differential Forms
In this paper, we present a numerical technique for performing Lie advection
of arbitrary differential forms. Leveraging advances in high-resolution finite
volume methods for scalar hyperbolic conservation laws, we first discretize the
interior product (also called contraction) through integrals over Eulerian
approximations of extrusions. This, along with Cartan's homotopy formula and a
discrete exterior derivative, can then be used to derive a discrete Lie
derivative. The usefulness of this operator is demonstrated through the
numerical advection of scalar fields and 1-forms on regular grids.Comment: Accepted version; to be published in J. FoC
Invariant expansion for the trigonal band structure of graphene
We present a symmetry analysis of the trigonal band structure in graphene,
elucidating the transformational properties of the underlying basis functions
and the crucial role of time-reversal invariance. Group theory is used to
derive an invariant expansion of the Hamiltonian for electron states near the K
points of the graphene Brillouin zone. Besides yielding the characteristic
k-linear dispersion and higher-order corrections to it, this approach enables
the systematic incorporation of all terms arising from external electric and
magnetic fields, strain, and spin-orbit coupling up to any desired order.
Several new contributions are found, in addition to reproducing results
obtained previously within tight-binding calculations. Physical ramifications
of these new terms are discussed.Comment: 10 pages, 1 figure; expanded version with more details and additional
result
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