Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves

Details Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves

1998-05-28

arxiv.org/abs/hep-th/9805206v2

JHEP 9807 (1998) 012

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 2 embedded figures, some spurious U(1)'s removed

Scientific paper

10.1088/1126-6708/1998/07/012

We consider the F-theory description of non-simply-connected gauge groups appearing in the E8 x E8 heterotic string. The analysis is closely tied to the arithmetic of torsion points on an elliptic curve. The general form of the corresponding elliptic fibration is given for all finite subgroups of E8 which are applicable in this context. We also study the closely-related question of point-like instantons on a K3 surface whose holonomy is a finite group. As an example we consider the case of the heterotic string on a K3 surface having the E8 gauge symmetry broken to (E6 x SU(3))/Z3 or SU(9)/Z3 by point-like instantons with Z3 holonomy.

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