Noncritical-Topological Correspondence: Disc Amplitudes and Noncompact   Branes
  We examine the duality between type 0 noncritical strings and topological B-model strings, with special emphasis on the flux dependence. The former theory is known to exhibit holomorphic factorisation upto a subtle flux-dependent disc term. We give a precise definition of the B-model dual and propose that it includes both compact and noncompact B-branes. The former give the factorised part of the free energy, while the latter violate holomorphic factorisation and contribute the desired disc term. These observations are generalised to rational radii, for which we derive a nonperturbatively exact result. We also show that our picture extends to a proposed alternative topological-anti-topological picture of the correspondence for type 0 strings. 
Anindya Mukherjee, Sunil Mukhi, Rahul Nigam