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We test Kim, Shiu and Vafa consistency conditions for six dimensional supergravity theories in explicit orientifold models. Based on the perturbative data, we conjecture the existence of null charges Q·Q= 0 for models with at least one tensor multiplet, coupling to string defects of charge Q. We use the new constraint to exclude some six-dimensional supersymmetric anomaly-free examples that have currently no string or F-theory realization. We also investigate the constraints in case where supersymmetry is broken in tachyon free vacua, with the breaking localised on antibranes.
Davide Cassani