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Frontiers in Number Theory, Physics, and Geometry II

On Conformal Field Theories, Discrete Groups and Renormalization

  • Pierre Cartier
  • Pierre Moussa
  • Bernard Julia
  • Pierre Vanhove
Book

Table of contents

  1. Front Matter
    Pages I-XXVIII
    PDF

  2. Conformal Field Theories for Strings and Branes

    1. Front Matter
      Pages I-XXVIII
      PDF
    2. The Dilogarithm Function
      Don Zagier
      Pages 3-65
    3. Conformal Field Theory and Torsion Elements of the Bloch Group
      Werner Nahm
      Pages 67-132
    4. Tracks, Lie's, and Exceptional Magic
      Predrag Cvitanović
      Pages 133-160
    5. Gauge Theories from D Branes
      Paolo Di Vecchia, Antonella Liccardo
      Pages 161-222
    6. On Superconformal Field Theories Associated to Very Attractive Quartics
      Katrin Wendland
      Pages 223-244

  3. Discrete Groups and Automorphic Forms

    1. Front Matter
      Pages I-XXVIII
      PDF
    2. An Introduction to Arithmetic Groups
      Christophe Soulé
      Pages 247-276
    3. Automorphic Forms: A Physicist's Survey
      Boris Pioline, Andrew Waldron
      Pages 277-302
    4. Strings and Arithmetic
      Gregory Moore
      Pages 303-359
    5. Modular Curves, C*-algebras, and Chaotic Cosmology
      Matilde Marcolli
      Pages 361-372
    6. Replicable Functions: An Introduction
      John McKay, Abdellah Sebbar
      Pages 373-386
    7. Lectures on the Langlands Program and Conformal Field Theory
      Edward Frenkel
      Pages 387-533

  4. Hopf Algebras and Renormalization

    1. Front Matter
      Pages I-XXVIII
      PDF
    2. A Primer of Hopf Algebras
      Pierre Cartier
      Pages 537-615
    3. Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory
      Alain Connes, Matilde Marcolli
      Pages 617-713
    4. Factorization in Quantum Field Theory: An Exercise in Hopf Algebras and Local Singularities
      Dirk Kreimer
      Pages 715-736
    5. Algebraic Algorithms in Perturbative Calculations
      Stefan Weinzierl
      Pages 737-757
    6. Multiple Logarithms, Algebraic Cycles and Trees
      H. Gangl, A.B. Goncharov, A. Levin
      Pages 759-774
  5. Back Matter
    Pages 775-789
    PDF

About this book

Keywords

Conformal field theory Prime discrete groups number theory renormalization

Editors and affiliations

  • Pierre Cartier
    • 1
  • Pierre Moussa
    • 2
  • Bernard Julia
    • 3
  • Pierre Vanhove
    • 4
  1. 1.I.H.E.S.Bures-sur-YvetteFrance
  2. 2.Service de Physique ThéoriqueCEA/SaclayGif-sur-YvetteFrance
  3. 3.LPTENSParisFrance
  4. 4.Service de Physique ThéoriqueCEA/SaclayGif-sur-YvetteFrance

Bibliographic information