ANOMALIES, DUALITIES, AND TOPOLOGY OF D=6 N=1 SUPERSTRING VACUA

We consider various aspects of compactifications of the Type I/heterot ic Spin(32)/Z(2) theory on K3. One family of such compactifications in cludes the standard embedding of the spin connection in the gauge grou p, and is on the same moduli space as the compactification of the hete rotic E(8) X E(8) theory on K3 with instanton numbers (8,16). Another class, which includes an orbifold of the Type I theory recently constr ucted by Gimon and Polchinski and whose field theory limit involves so me topological novelties, is on the moduli space of the heterotic E(8) x E(8) theory on K3 with instanton numbers (12,12). These connections between Spin(32)/Z(2) and E(8) x E(8) models can be demonstrated by T -duality, and permit a better understanding of nonperturbative gauge f ields in the (12,12) model. In the transformation between Spin(32)/Z(2 ) and E(8) x E(8) models, the strong/weak coupling duality of the (12, 12) E(8) X E(8) model is mapped to T-duality in the Type I theory. The gauge and gravitational anomalies in the Type I theory are canceled b y an extension of the Green-Schwarz mechanism.