1,256 research outputs found
Large Chiral Diffeomorphisms on Riemann Surfaces and W-algebras
The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a
complex scalar field over a Riemann surface is presented in the paper under the
name of large diffeomorphisms. After an heuristic approach, we show how a
linear truncation in the Taylor expansion can generate an algebra of symmetry
characterized by some structure functions. Such a linear truncation is
explicitly realized by introducing the notion of Forsyth frame over the Riemann
surface with the help of a conformally covariant algebraic differential
equation. The large chiral diffeomorphism action is then implemented through a
B.R.S. formulation (for a given order of truncation) leading to a more
algebraic set up. In this context the ghost fields behave as holomorphically
covariant jets. Subsequently, the link with the so called W-algebras is made
explicit once the ghost parameters are turned from jets into tensorial ghost
ones. We give a general solution with the help of the structure functions
pertaining to all the possible truncations lower or equal to the given order.
This provides another contribution to the relationship between KdV flows and
W-diffeomorphimsComment: LaTeX file, 31 pages, no figure. Version to appear in J. Math. Phys.
Work partly supported by Region PACA and INF
From the 'cinematic' to the 'anime-ic': Issues of movement in anime
This is the author's accepted manuscript. The final published article is available from the link below.This article explores the way that movement is formally depicted in anime. Drawing on Thomas Lamarre's concepts of the `cinematic' and the `anime-ic', the article interrogates further the differences in movement and action in anime from traditional filmic form. While often considered in terms of `flatness', anime offers spectacle, character development and, ironically, depth through the very form of movement put to use in such texts.The article questions whether the modes of address at work in anime are unique to this form of animation.Taking into account how the terms `cinematic' and `anime-ic' can be understood (and by extension the cinematic and animatic apparatus), the article also begins to explore how viewers might identify with such images
Menelaus relation and Fay's trisecant formula are associativity equations
It is shown that the celebrated Menelaus relation and Fay's trisecant formula
similar to the WDVV equation are associativity conditions for structure
constants of certain three-dimensional algebra.Comment: Talk given at the Conference " Mathematics and Physics of Solitons
and Integrable Systems", Dijon, 28.6-2.7, 2009. Minor misprints correcte
Determinantal Characterization of Canonical Curves and Combinatorial Theta Identities
We characterize genus g canonical curves by the vanishing of combinatorial
products of g+1 determinants of Brill-Noether matrices. This also implies the
characterization of canonical curves in terms of (g-2)(g-3)/2 theta identities.
A remarkable mechanism, based on a basis of H^0(K_C) expressed in terms of
Szego kernels, reduces such identities to a simple rank condition for matrices
whose entries are logarithmic derivatives of theta functions. Such a basis,
together with the Fay trisecant identity, also leads to the solution of the
question of expressing the determinant of Brill-Noether matrices in terms of
theta functions, without using the problematic Klein-Fay section sigma.Comment: 35 pages. New results, presentation improved, clarifications added.
Accepted for publication in Math. An
Potential glucose monitoring of blood plasma using hollow core photonic crystal fibre
The ratio (ζ) of surface tension to viscosity of liquids can be determined using hollow core photonic crystal fibres (HCPCF), and we show here techniques to determine ζ of glucose levels within fluids, of nano-litre quantities. We demonstrate an optically integrated micro-capillary viscometer, to determine the concentrations of nano-litre solutions based on properties of their flow within HC-PCF. The filling of the fibres with liquids within a given range of refractive index will induce a shift in the photonic band gap of the fibre, allowing guidance of light at wavelengths that were originally outside the bandgap of the HC-PCF
Induced quantum gravity on a Riemann Surface
Induced quantum gravity dynamics built over a Riemann surface is studied in
arbitrary dimension. Local coordinates on the target space are given by means
of the Laguerre-Forsyth construction. A simple model is proposed and
pertubatively quantized. In doing so, the classical W-symmetry turns out to be
preserved on-shell at any order of the perturbative expansion. As a
main result, due to quantum corrections, the target coordinates acquire a
non-trivial character.Comment: LaTex, 32 pages, no figures, submitted to Int. J. Mod. Phys.
A Class of Topological Actions
We review definitions of generalized parallel transports in terms of
Cheeger-Simons differential characters. Integration formulae are given in terms
of Deligne-Beilinson cohomology classes. These representations of parallel
transport can be extended to situations involving distributions as is
appropriate in the context of quantized fields.Comment: 41 pages, no figure
Deformation Theory of Holomorphic Vector Bundles, Extended Conformal Symmetry and Extensions of 2D Gravity
Developing on the ideas of R. Stora and coworkers, a formulation of two
dimensional field theory endowed with extended conformal symmetry is given,
which is based on deformation theory of holomorphic and Hermitian spaces. The
geometric background consists of a vector bundle over a closed surface
endowed with a holomorphic structure and a Hermitian structure
subordinated to it. The symmetry group is the semidirect product of the
automorphism group of and the extended Weyl group of and acts on the holomorphic and Hermitian structures. The
extended Weyl anomaly can be shifted into an automorphism chirally split
anomaly by adding to the action a local counterterm, as in ordinary conformal
field theory. The dependence on the scale of the metric on the fiber of is
encoded in the Donaldson action, a vector bundle generalization of the
Liouville action. The Weyl and automorphism anomaly split into two
contributions corresponding respectively to the determinant and
projectivization of . The determinant part induces an effective ordinary
Weyl or diffeomorphism anomaly and the induced central charge can be computed.Comment: 49 pages, plain TeX. A number of misprints have been correcte
Chern-Simons States at Genus One
We present a rigorous analysis of the Schr\"{o}dinger picture quantization
for the Chern-Simons theory on 3-manifold torusline, with
insertions of Wilson lines. The quantum states, defined as gauge covariant
holomorphic functionals of smooth -connections on the torus, are
expressed by degree theta-functions satisfying additional conditions. The
conditions are obtained by splitting the space of semistable
-connections into nine submanifolds and by analyzing the behavior of
states at four codimension strata. We construct the
Knizhnik-Zamolodchikov-Bernard connection allowing to compare the states for
different complex structures of the torus and different positions of the Wilson
lines. By letting two Wilson lines come together, we prove a recursion relation
for the dimensions of the spaces of states which, together with the (unproven)
absence of states for spins\s>{_1\over^2}level implies the Verlinde dimension
formula.Comment: 33 pages, IHES/P
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