Conformal Field Theory II: Lattices and Kač-Moody Algebras

  • Ralph Blumenhagen
  • Dieter Lüst
  • Stefan Theisen
Part of the Theoretical and Mathematical Physics book series (TMP)


In the previous chapter we have learned that in toroidal compactifications of the bosonic string there are, in addition to the Kaluza-Klein gauge bosons familiar from field theory, further massless vectors of purely stringy origin. However, we did not show that these massless vectors are gauge bosons of a non-Abelian gauge group G, transforming in the adjoint representation. The necessary mathematical tool to do this is the theory of infinite dimensional (current) algebras, the so-called affine Kač-Moody algebras. They are the subject of this chapter for which we assume some familiarity with the structure of finite dimensional Lie algebras.


Partition Function Root Lattice Conjugacy Class Vertex Operator Heterotic String 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ralph Blumenhagen
    • 1
  • Dieter Lüst
    • 2
  • Stefan Theisen
    • 3
  1. 1.Werner-Heisenberg-Institut Max-Planck-Institut für PhysikMünchenGermany
  2. 2.Arnold-Sommerfeld Zentrum für Theoretische PhysikLudwig-Maximilians Universität MünchenMünchenGermany
  3. 3.Albert-Einstein-Institut Max-Planck-Institut für GravitationsphysikGolmGermany

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