Anomalies, dualities, and topology of D = 6 N = 1 superstring vacua

We consider various aspects of compactifications of the Type I/heterotic Spin(32)/ℤ₂ theory on K3. One family of such compactifications includes the standard embedding of the spin connection in the gauge group, and is on the same moduli space as the compactification of the heterotic E₈ × E₈ theory on K3 with instanton numbers (8,16). Another class, which includes an orbifold of the Type I theory recently constructed by Gimon and Polchinski and whose field theory limit involves some topological novelties, is on the moduli space of the heterotic E₈ × E₈ theory on K3 with instanton numbers (12,12). These connections between Spin(32)/ℤ₂ and E₈ × E₈ models can be demonstrated by T-duality, and permit a better understanding of nonperturbative gauge fields in the (12,12) model. In the transformation between Spin(32)/ℤ₂ and E₈ × E₈ models, the strong/weak coupling duality of the (12,12) E₈ × E₈ model is mapped to T-duality in the Type I theory. The gauge and gravitational anomalies in the Type I theory are canceled by an extension of the Green - Schwarz mechanism.