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 $q$-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

Twenty years of JHEP

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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

string field theory a short introduction

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