String theory and algebraic geometry of moduli spaces
Abstract
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 parameterized by moduli space. As a result the partition function is written 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 field K, a connection between string theory and the infinite primes of K is established. It is conjectured that the usual partition function is a special case of a partition function on the moduli space defined over K.
- Publication:
-
Unknown
- Pub Date:
- July 1987
- Bibcode:
- 1987stag.rept.....S
- Keywords:
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- Field Theory (Algebra);
- Riemann Manifold;
- String Theory;
- Green'S Functions;
- Operators (Mathematics);
- Parameterization;
- Thermodynamics and Statistical Physics