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

Abstract

We consider various aspects of compactifications of the Type I/heterotic Spin(32)/Z 2 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 E 8 × E 8 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 E 8 × E 8 theory on K3 with instanton numbers (12,12). These connections between Spin(32)/Z 2 and E 8 × E 8 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)/Z 2 and E 8 × E 8 models, the strong/weak coupling duality of the (12,12) E 8 × 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 by an extension of the Green-Schwarz mechanism.

Lectures on superstring and M theory dualities

“…[84] However, this blowup does not give the n 1 = 16, n 5 = 8 model described in subsection 2. The reason for this is that the instantons are embedded in the SO(32) group differently than they were in the examples discussed previously.…”

“…Both kinds of heterotic strings, F and D, are solitons (D-branes, in fact) of the type I description. [84] One corresponds to the 10d heterotic string and the other corresponds to the dual 10d 5-brane wrapped on the orbifold. T duality interchanges these two solitons.…”

Fixing All Moduli in a Simple F-Theory Compactification

“…Thus, for the symmetric resolution, in our normalization conventions, the dimensionless superpotential W (see appendix A) we consider is: 13) where W 0 is the flux contribution discussed in section 5. There can be higher order terms, for example from multi-wrapped instantons.…”

Branes and the gauge hierarchy

“…Notice that the U (1) 2 factors become massive by mixing with bulk tensor hypermultiplets [23], so their apparent non-vanishing β-functions can be understood through the exchange of this hypermultiplet.…”