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


In the first part of this chapter we compute the one-loop partition function of the closed fermionic string. We will do this in light cone gauge. The possibility to assign to the world-sheet fermions periodic or anti-periodic boundary conditions leads to the concept of spin structures. The requirement of modular invariance is then shown to result in the GSO projection. We also generalize some of the results of Chap. 6 to the case of fermions. We then consider open superstrings, i.e. we extend the formalism of conformal field theories with boundaries to include free fermionic fields. This gives rise to D-branes in superstring theories. We also discuss non-oriented superstrings, which result form performing a quotient of the type IIB superstring by the world-sheet parity transformation. We show that one-loop diagrams are divergent unless D-branes are present in the model. This defines the type I superstring, whose construction we discuss in some detail.


Partition Function Open String Spin Structure Closed String Modular Transformation 
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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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