Can a Lattice String Have a Vanishing Cosmological Constant?
  We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must satisfy. 
Terry Gannon (Carleton University) and C.S. Lam (McGill University)