Contents Online

# Advances in Theoretical and Mathematical Physics

## Volume 25 (2021)

### Number 5

### Heterotic/$F$-theory duality and Narasimhan–Seshadri equivalence

Pages: 1199 – 1233

DOI: https://dx.doi.org/10.4310/ATMP.2021.v25.n5.a2

#### Authors

#### Abstract

Finding the $F$-theory dual of a Heterotic model with Wilson-line symmetry breaking presents the challenge of achieving the dual $\mathbb{Z}_2$-action on the $F$-theory model in such a way that the $\mathbb{Z}_2$-quotient is Calabi–Yau with an Enriques GUT surface over which $SU(5)_{\operatorname{gauge}}$ symmetry is maintained. We propose a new way to approach this problem by taking advantage of a little-noticed choice in the application of Narasimhan–Seshadri equivalence between real $E_8$-bundles with Yang–Mills connection and their associated complex holomorphic $E^\mathbb{C}_8$-bundles, namely the one given by the real outer automorphism of $E^\mathbb{C}_8$ by complex conjugation. The triviality of the restriction on the compact real form $E_8$ allows one to introduce it into the $\mathbb{Z}_2$-action, thereby restoring $E_8$- and hence $SU(5)_{\operatorname{gauge}}$-symmetry on which the Wilson line can be wrapped.

S.R. acknowledges partial support from Department of Energy grant DE-SC0011726.

Published 17 June 2022