Communications in Mathematical Physics

, Volume 114, Issue 4, pp 645–685 | Cite as

String theory and algebraic geometry of moduli spaces

  • Dirk-Jan Smit


It is shown how the algebraic geometry of the moduli space of Riemann surfaces entirely determines the partition function of Polyakov's string theory. This is done by using elements of Arakelov's intersection theory applied to determinants of families of differential operators parametrized by moduli space. As a result we write the partition function in terms of exponentials of Arakelov's Green functions and Faltings' invariant on Riemann surfaces. Generalizing to arithmetic surfaces, i.e. surfaces which are associated to an algebraic number fieldK, we establish a connection between string theory and the infinite primes ofK. As a result we conjecture that the usual partition function is a special case of a new partition function on the moduli space defined overK.


Neural Network Statistical Physic Complex System String Theory Partition Function 
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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Dirk-Jan Smit
    • 1
  1. 1.Institute for Theoretical PhysicsUtrechtThe Netherlands

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