Orbifolds of M-theory and type II string theories in two dimensions

We consider several orbifold compactifications of M-theory and their corresponding type II duals in two space-time dimensions. In particular, we show that while the orbifold compactification of M-theory on T-9/T9 is dual to the orbifold compactification of type IIB string theory on T-8/I8, the same orbifold T-8/I-8 of type ITA string theory is dual to M-theory compactified on a smooth product manifold K3 x T-5. Similarly, while the orbifold compactification of M-theory on (K3 T-5)/sigma . T5 is dual to the orbifold compactification of type IIB string theory on (K3 x T-4)/sigma . I4, the same orbifold of type IIA string theory is dual to the orbifold T-4 x (K3 x S-1)/sigma . T1 of M-theory. The spectrum of various orbifold compactifications of M-theory and type II string theories on both sides are compared giving evidence in favor of these duality conjectures. We also comment on a connection between the Dasgupta-Mukhi-Witten conjecture and the Dabholkar-Park-Sen conjecture for the six-dimensional orbifold models of type IIB string theory and M-theory. (C) 1997 Elsevier Science B.V.