We study some aspects of 2D supersymmetric sigma models on orbifolds. It turns out that independently of whether the 2D QFT is conformal the operator products of twist operators are non-singular, suggesting that massive (non-conformal) orbifolds also "resolve singularities" just as in the conformal case. Moreover we recover the OPE of twist operators for conformal theories by considering the uv limit of the massive orbifold correlation functions. Alternatively, we can use the OPE of twist fields at the conformal point to derive conditions for the existence of non-singular solutions to special nonlinear differential equations (such as Painleve III).
