7,131 research outputs found
The role of the Beltrami parametrization of complex structures in 2-d Free Conformal Field Theory
This talk gives a review on how complex geometry and a Lagrangian formulation
of 2-d conformal field theory are deeply related. In particular, how the use of
the Beltrami parametrization of complex structures on a compact Riemann surface
fits perfectly with the celebrated locality principle of field theory, the
latter requiring the use infinite dimensional spaces. It also allows a direct
application of the local index theorem for families of elliptic operators due
to J.-M. Bismut, H. Gillet and C. Soul\'{e}. The link between determinant line
bundles equipped with the Quillen\'s metric and the so-called holomorphic
factorization property will be addressed in the case of free spin b-c
systems or more generally of free fields with values sections of a holomorphic
vector bundles over a compact Riemann surface.Comment: Actes du Colloque "Complex Geometry '98
Who cried for Argentina? Notes on the 2001-02 Crisis
In the midst of the current global slowdown this paper revisits Argentina’s dismal experience in the 1990s with a complete embrace of globalisation, the crisis of 2001-02 and its subsequent recovery.Argentine; Economic; Crisis;
Spherical Designs and Heights of Euclidean Lattices
We study the connection between the theory of spherical designs and the
question of extrema of the height function of lattices. More precisely, we show
that a full-rank n-dimensional Euclidean lattice, all layers of which hold a
spherical 2-design, realises a stationary point for the height function, which
is defined as the first derivative at 0 of the spectral zeta function of the
associated flat torus. Moreover, in order to find out the lattices for which
this 2-design property holds, a strategy is described which makes use of theta
functions with spherical coefficients, viewed as elements of some space of
modular forms. Explicit computations in dimension up to 7, performed with
Pari/GP and Magma, are reported.Comment: 22 page
The Analogue Computer as a Voltage-Controlled Synthesiser
This paper re-appraises the role of analogue computers within electronic and
computer music and provides some pointers to future areas of research. It
begins by introducing the idea of analogue computing and placing in the context
of sound and music applications. This is followed by a brief examination of the
classic constituents of an analogue computer, contrasting these with the
typical modular voltage-controlled synthesiser. Two examples are presented,
leading to a discussion on some parallels between these two technologies. This
is followed by an examination of the current state-of-the-art in analogue
computation and its prospects for applications in computer and electronic
music
Diffeomorphism Cohomology in Beltrami Parametrization II : The 1-Forms
We study the 1-form diffeomorphism cohomologies within a local conformal
Lagrangian Field Theory model built on a two dimensional Riemann surface with
no boundary. We consider the case of scalar matter fields and the complex
structure is parametrized by Beltrami differential. The analysis is first
performed at the Classical level, and then we improve the quantum extension,
introducing the current in the Lagrangian dynamics, coupled to external source
fields. We show that the anomalies which spoil the current conservations take
origin from the holomorphy region of the external fields, and only the
differential spin 1 and 2 currents (as well their c.c) could be anomalous.Comment: 39 pages,CPT-94/P.3072,LaTe
The Performance Implications of Membership in Competing Firm Constellations: Evidence from the Global Airline Industry
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