New Branches of String Compactifications and their F-Theory Duals

TL;DR

The paper builds new branches of heterotic $E_8 imes E_8$ compactifications by incorporating $H imes U(1)^{8-d}$ backgrounds, and derives their precise F-theory and Type IIA dual descriptions via elliptic fibrations over Hirzebruch bases $IF_n$. By pairing each heterotic chain (A, B, C, D) with a corresponding elliptic fiber (IP$_2^{(1,2,3)}[6]$, IP$_2^{(1,1,2)}[4]$, IP$_2^{(1,1,1)}[3]$, IP$_3^{(1,1,1,1)}[2,2]$), the authors obtain explicit F-theory duals and demonstrate consistent matching of spectra and Hodge numbers across dual theories, including conifold and phase transitions. The work reveals a rich web of six- and four-dimensional dualities, where anomalous $U(1)$ factors can become massive via coupling to $B_{MN}$ and where transitions between models with different tensor multiplet content ($n_T$) occur through tensionless-string dynamics. Overall, the study extends the landscape of dual pairs, clarifies how elliptic-fiber choices control dual gauge structures, and provides concrete tools for mapping heterotic chains to F-theory and Type II geometries with broad implications for string-duality networks.

Abstract

We study heterotic $E_8\times E_8$ models that are dual to compactifications of F-theory and type IIA string on certain classes of elliptically fibered Calabi-Yau manifolds. Different choices for the specific torus in the fibration have heterotic duals that are most easily understood in terms of $E_8\times E_8$ models with gauge backgrounds of type $H\times U(1)^{8-d}$, where $H$ is a non-Abelian factor. The case with $d=8$ corresponds to the well known $E_8\times E_8$ compactifications with non-Abelian instanton backgrounds $(k_1,k_2)$ whose F-theory duals are built through compactifications on fibrations of the torus $\IP_2^{(1,2,3)}[6]$ over $\IF_n$. The new cases with $d < 8$ correspond to other choices for the elliptic fiber over the same base and yield unbroken $U(1)$'s, some of which are anomalous and acquire a mass by swallowing zero modes of the antisymmetric $B_{MN}$ field. We also study transitions to models with no tensor multiplets in $D=6$ and find evidence of $E_d$ instanton dynamics. We also consider the possibility of conifold transitions among spaces with different realization of the elliptic fiber.