52 research outputs found
String Partition Functions, Hilbert Schemes, and Affine Lie Algebra Representations on Homology Groups
This review paper contains a concise introduction to highest weight
representations of infinite dimensional Lie algebras, vertex operator algebras
and Hilbert schemes of points, together with their physical applications to
elliptic genera of superconformal quantum mechanics and superstring models. The
common link of all these concepts and of the many examples considered in the
paper is to be found in a very important feature of the theory of infinite
dimensional Lie algebras: the modular properties of the characters (generating
functions) of certain representations. The characters of the highest weight
modules represent the holomorphic parts of the partition functions on the torus
for the corresponding conformal field theories. We discuss the role of the
unimodular (and modular) groups and the (Selberg-type) Ruelle spectral
functions of hyperbolic geometry in the calculation of elliptic genera and
associated -series. For mathematicians, elliptic genera are commonly
associated to new mathematical invariants for spaces, while for physicists
elliptic genera are one-loop string partition function (therefore they are
applicable, for instance, to topological Casimir effect calculations). We show
that elliptic genera can be conveniently transformed into product expressions
which can then inherit the homology properties of appropriate polygraded Lie
algebras.Comment: 56 pages, review paper, in honour of J.S.Dowker. arXiv admin note:
text overlap with arXiv:0905.1285, arXiv:math/0006201, arXiv:math/0412089,
arXiv:math/0403547 by other author
L'Informazione Scientifica e Internet:l'esperienza della SISSA
ItViene ripercorsa la storia dell'avvento di internet in una istituzione scientifica come la SISSA di Trieste con le modificazioni indotte e le realizzazioni che ha permesso. Viene illustrato in particolare il progetto Ulisse, per la divulgazione dell'informazione scientifica via internet, i servizi messi a disposizione e l'organizzazione che richiede
Regularization of energy-momentum tensor correlators and parity-odd terms
We discuss the problem of regularizing correlators in conformal field
theories. The only way to do it in coordinate space is to interpret them as
distributions. Unfortunately except for the simplest cases we do not have
tabulated mathematical results. The way out we pursue here is to go to momentum
space and use Feynman diagram techniques and their regularization methods. We
focus on the energy-momentum tensor correlators and, to gain insight, we
compute and regularize 2-point functions in 2d with various techniques both in
coordinate space and in momentum space, obtaining the same results. Then we do
the same for 2-point functions in 4d. Finally we turn to 3-point function in
4d, and concentrate on the parity-odd part. We derive in particular the
regularized trace and divergence of the energy-momentum tensor in a chiral
fermion model. We discuss the problems related to the parity-odd trace anomaly.Comment: 40 pages, 1 figure. v2: minor changes and typos correcte
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