F-theory at constant coupling

The subspace of the moduli space of F-theory on K3 over which the coupling remains constant develops new branches at special values of this coupling. These values correspond to fixed points under the SL(2, Z) duality group of the type IIB string. The branches contain points where K3 degenerates to orbifolds of the four-torus by Z(3), Z(4) and Z(6). A singularity analysis shows that exceptional group symmetries appear on these branches, including pure E(8) x E(8), although SO(32) cannot be realised in this way. The orbifold points can be mapped to a kind of non-perturbative generalization of a IIB orientifold, and to M-theory orbifolds with non-trivial action on 2-brane wrapping modes.