## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 18, Number 6 (2014), 1463-1503.

### Building blocks for generalized heterotic/F-theory duality

Jonathan J. Heckman, Hai Lin, and Shing-Tung Yau

#### Abstract

In this note we propose a generalization of heterotic/F-theory duality. We introduce a set of non-compact building blocks which we glue together to reach compact examples of generalized duality pairs. The F-theory building blocks consist of non-compact elliptically fibered Calabi-Yau fourfolds which also admit a $K3$ fibration. The compact elliptic model obtained by gluing need not have a globally defined $K3$ fibration. By replacing the $K3$ fiber of each F-theory building block with a $T^2$, we reach building blocks in a heterotic dual vacuum which includes a position dependent dilaton and three-form flux. These building blocks are glued together to reach a heterotic flux background. We argue that in these vacua, the gauge fields of the heterotic string become localized, and remain dynamical even when gravity decouples. This enables a heterotic dual for the hyperflux GUT breaking mechanism which has recently figured prominently in F-theory GUT models. We illustrate our general proposal with some explicit examples.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 18, Number 6 (2014), 1463-1503.

**Dates**

First available in Project Euclid: 4 December 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1417707824

**Mathematical Reviews number (MathSciNet)**

MR3285614

**Zentralblatt MATH identifier**

1308.81147

#### Citation

Heckman, Jonathan J.; Lin, Hai; Yau, Shing-Tung. Building blocks for generalized heterotic/F-theory duality. Adv. Theor. Math. Phys. 18 (2014), no. 6, 1463--1503. https://projecteuclid.org/euclid.atmp/1417707824