F-theory and the Gimon-Polchinski Orientifold

TL;DR

This work proves the equivalence between the Gimon-Polchinski orientifold and F-theory on an elliptically fibered Calabi-Yau threefold over $CP^1×CP^1$ by aligning gauge-structure breaking, local moduli deformations, and axion-dilaton backgrounds in the weak coupling regime. It constructs an explicit map between deformations in the GP model (blow-up modes and vevs of open-string states) and corresponding F-theory deformations through tailored Weierstrass data and discriminant factorization, achieving a one-to-one correspondence including symmetry-enhancement loci. The analysis also explains an apparent constant-coupling discrepancy via non-perturbative effects and B-field flux, clarifying the role of flux in restricting gauge enhancements on the GP side. Finally, it links non-perturbative corrections to the global geometry of intersecting orientifolds and D-branes, and discusses implications for four-dimensional dualities and three-brane probe dynamics.

Abstract

We establish the equivalence of the Gimon-Polchinski orientifold and F-theory on an elliptically fibered Calabi-Yau three fold on base $CP^1 \times CP^1$ by comparing the gauge symmetry breaking pattern, local deformations in the moduli space, as well as the axion-dilaton background in the weak coupling limit in the two theories. We also provide an explanation for an apparent discrepancy between the F-theory and the orientifold results for constant coupling configuration.