Number of massless fermion families in superstring theory
Abstract
In any KaluzaKlein compactification of the tendimensional superstring theory we relate the number of families to the index of an appropriate Dirac operator. By using the AtiyahSinger index theorem the number of families is then related to an integral involving the gauge fields only. The number of families is not necessarily related to the Euler characteristics of the compact manifold for compactifications that admit nonzero torsion or a spin connection which is not embedded in the gauge group (a complete solution of this type has not yet been displayed). Our result applies to the general situation.
 Publication:

Physics Letters B
 Pub Date:
 November 1985
 DOI:
 10.1016/03702693(85)902047
 Bibcode:
 1985PhLB..163..118B