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New Solutions to the $G_2$ Hull-Strominger System via torus fibrations over $K3$ orbifolds

Anna Fino, Gueo Grantcharov, Jose Medel

TL;DR

This work constructs new smooth solutions to the $G_2$ Hull-Strominger system on seven-manifolds that are total spaces of principal $T^3$- orbi-bundles over singular K3 surfaces. By combining Seifert $S^1$-bundle data from three primitive divisors on a blown-up K3 orbisurface with a stable rank-$2$ bundle via a singular Serre construction, the authors assemble a $G_2$-structure $\varphi_{u,t}$ and a hyperholomorphic gauge connection to satisfy the system, including the anomaly cancellation balance via an explicit choice of the parameter $t$. The main theorem guarantees the existence of solutions for each suitable $c_2(V)\ge5$, and the paper provides concrete realizations using Iano-Fletcher’s hypersurface families $X_{30}, X_{36}, X_{50}$, yielding simply-connected 7-manifolds with prescribed Betti numbers that carry $G_2$ Hull-Strominger vacua. This work broadens the landscape of heterotic $G_2$ compactifications by linking orbifold K3 geometry, Seifert bundle theory, and stable bundle techniques to produce new explicit vacua with controlled topology.

Abstract

Using torus fibrations over K3 orbisurfaces, we construct new smooth solutions to the $G_2$ Hull-Strominger system. These manifolds arise as total spaces of principal $T^3$ (orbi)bundles over singular K3 surfaces. Our construction is based on the choice of three divisors on a singular K3 surface that are primitive with respect to a particular Kählermetric. The stable bundle is obtained via an adaptation of the Serre construction to the singular setting.

New Solutions to the $G_2$ Hull-Strominger System via torus fibrations over $K3$ orbifolds

TL;DR

This work constructs new smooth solutions to the Hull-Strominger system on seven-manifolds that are total spaces of principal - orbi-bundles over singular K3 surfaces. By combining Seifert -bundle data from three primitive divisors on a blown-up K3 orbisurface with a stable rank- bundle via a singular Serre construction, the authors assemble a -structure and a hyperholomorphic gauge connection to satisfy the system, including the anomaly cancellation balance via an explicit choice of the parameter . The main theorem guarantees the existence of solutions for each suitable , and the paper provides concrete realizations using Iano-Fletcher’s hypersurface families , yielding simply-connected 7-manifolds with prescribed Betti numbers that carry Hull-Strominger vacua. This work broadens the landscape of heterotic compactifications by linking orbifold K3 geometry, Seifert bundle theory, and stable bundle techniques to produce new explicit vacua with controlled topology.

Abstract

Using torus fibrations over K3 orbisurfaces, we construct new smooth solutions to the Hull-Strominger system. These manifolds arise as total spaces of principal (orbi)bundles over singular K3 surfaces. Our construction is based on the choice of three divisors on a singular K3 surface that are primitive with respect to a particular Kählermetric. The stable bundle is obtained via an adaptation of the Serre construction to the singular setting.
Paper Structure (6 sections, 8 theorems, 49 equations, 1 table)

This paper contains 6 sections, 8 theorems, 49 equations, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries on K3 Orbifolds and $S^1$ Seifert bundles
  3. An ansatz on $T^3$-fibrations over $K3$ orbifolds
  4. Divisors and stable bundles on K3 orbisurfaces
  5. Main results
  6. Examples

Key Result

Theorem 2.1

Let $X$ be a normal reduced complex space with at worst quotient singularities and $\Delta=\sum_i (1-\frac{1}{m_i})D_i$ be a $\mathbb{Q}$ divisor (this is the data associated to an orbifold). Then there is a one-to-one correspondence between Seifert ${\mathbb C}^*$-bundles $f:Y\rightarrow (X,\Delta)

Theorems & Definitions (12)

  • Definition 2.1
  • Definition 2.2
  • Theorem 2.1
  • Theorem 2.2
  • Lemma 4.1
  • proof
  • Lemma 4.2
  • Theorem 5.1
  • proof
  • Corollary 5.1
  • ...and 2 more