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 ⁹J₉ is dual to the orbifold compactification of type IIB string theory on T ⁸I₈, the same orbifold T ⁸J₈ of type IIA string theory is dual to M-theory compactified on a smooth product manifold K3 × T ⁵. Similarly, while the orbifold compactification of M-theory on (K3 × T ⁵)/ σ · J₅ is dual to the orbifold compactification of type IIB string theory on (K3 × T ⁴)/ σ · I₄, the same orbifold of type IIA string theory is dual to the orbifold T ⁴ × (K3 × S ¹)/ σ · J₁ 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 l and the Dabholkar-Park-Sen conjecture for the six-dimensional orbifold models of type IIB string theory and M-theory.