Anomalies, Dualities, and Topology of D=6 N=1 Superstring Vacua

TL;DR

This work analyzes D=6, N=1 vacua arising from Spin(32)/Z2 and E8×E8 compactifications on K3, focusing on two prominent constructions—Gimon-Polchinski’s Type I orbifold and the DMW symmetric E8×E8 embedding—and their interrelation via dualities. It demonstrates how perturbative anomalies factorize and are cancelled by a Green-Schwarz mechanism extended to twisted RR fields, while identifying a nonperturbative obstruction linked to vector structure and the second Stiefel-Whitney class. The paper develops two duality channels: Type I–heterotic SO(32) and heterotic SO(32)–E8×E8, with T-dualities mapping brane sectors to perturbative and nonperturbative gauge fields and correlating brane content to instanton data on ALE/K3 spaces; it further uses instanton moduli and eta invariants to classify allowed backgrounds. Collectively, these dualities and topological analyses clarify how GP and DMW vacua are connected, resolve puzzles about small instantons, and illuminate the landscape of six-dimensional vacua with one tensor multiplet. The results have broad significance for understanding nonperturbative gauge dynamics, duality symmetries, and the topology of string vacua in lower dimensions, with precise treatments of anomaly polynomials, twisted sector couplings, and instanton moduli on ALE/K3 spaces.

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 $E_8\times E_8$ 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 $E_8\times E_8$ theory on K3 with instanton numbers (12,12). These connections between $Spin(32)/\Z_2$ and $E_8\times E_8$ models can be demonstrated by T duality, and permit a better understanding of non-perturbative gauge fields in the (12,12) model. In the transformation between $Spin(32)/\Z_2$ and $E_8\times E_8$ models, the strong/weak coupling duality of the (12,12) $E_8\times E_8$ 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.