  We study interacting massive N=(2,2) supersymmetric field theories in two
dimensions which arise from deforming conformal field theories with a
continuous spectrum. Firstly, we deform N=2 superconformal Liouville theory
with relevant operators, and twist the theory into a topological quantum field
theory. These theories can be thought of as twisted Landau-Ginzburg models with
negative power superpotential. We determine the structure constants of the
chiral ring and therefore all correlators of these topological quantum field
theories. We provide general formulas for the deformed operators of given
charge as well as explicit solutions to the WDVV equations. Secondly, we
analyze the topological anti-topological sector of the theory. We compute the
metric at the conformal point through localization. Moreover, we show that the
topological-anti-topological fusion differential equations on the metric in a
family of non-compact theories takes the affine Toda form. The metric as a
function of the family of theories is identical to the metric in certain
deformed compact models. For a negative cubic power Landau-Ginzburg
superpotential, for instance, it is governed by the Painlev\'e III differential
equation.
