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On Vanishing Two Loop Cosmological Constants in Nonsupersymmetric Strings

It has recently been suggested that in certain special nonsupersymmetric type II string compactifications, at least the first two perturbative contributions to the cosmological constant $Λ$ vanish. Support for perturbative vanishing beyond 1-loop (as well as evidence for the absence of some nonperturbative contributions) has come from duality arguments. There was also a direct 2-loop computation which was incomplete; in this note we explain the deficiency of the previous 2-loop calculation and discuss the complete 2-loop computation in two different models. The corrected analysis yields a vanishing 2-loop contribution to $Λ$ in these models.