On S-duality for non-simply-laced gauge groups

Abstract

We point out that for Script N = 4 gauge theories with exceptional gauge groups G_2 and F_4 the S-duality transformation acts on the moduli space by a nontrivial involution. We note that the duality groups of these theories are the Hecke groups with elliptic elements of order 6 and 4, respectively. These groups extend the Γ_0(3) and Γ_0(2) subgroups of SL(2,ℤ) by elements with a non-trivial action on the moduli space. We show that under a certain embedding of these gauge theories into string theory, the Hecke duality groups are represented by T-duality transformations.