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On the Frozen F-theory Landscape

David R. Morrison, Benjamin Sung

Abstract

We study $6$d $\mathcal{N} = (1,0)$ supergravity theories arising in the frozen phase of F-theory. For each of the known global models, we construct an F-theory compactification in the unfrozen phase with an identical non-abelian gauge algebra and massless matter content. Two such low energy effective theories are then distinguished through gauge enhancements in moduli space. We study potentially new global models obtained via compact embeddings of a plethora of $6$d $\mathcal{N}= (1,0)$ superconformal field theories and little string theories constructed using frozen $7$-branes. In some cases, these provably do not exist, and in other cases, we explicitly construct a compact embedding, yielding $6$d supergravity theories with new massless spectra. Finally, by using gravitational anomaly cancellation, we conjecture the existence of localized neutral hypermultiplets along frozen $7$-brane loci.

On the Frozen F-theory Landscape

Abstract

We study d supergravity theories arising in the frozen phase of F-theory. For each of the known global models, we construct an F-theory compactification in the unfrozen phase with an identical non-abelian gauge algebra and massless matter content. Two such low energy effective theories are then distinguished through gauge enhancements in moduli space. We study potentially new global models obtained via compact embeddings of a plethora of d superconformal field theories and little string theories constructed using frozen -branes. In some cases, these provably do not exist, and in other cases, we explicitly construct a compact embedding, yielding d supergravity theories with new massless spectra. Finally, by using gravitational anomaly cancellation, we conjecture the existence of localized neutral hypermultiplets along frozen -brane loci.
Paper Structure (26 sections, 1 theorem, 53 equations, 6 tables)

This paper contains 26 sections, 1 theorem, 53 equations, 6 tables.

Table of Contents

  1. Introduction
  2. Summary of Results
  3. Consistency conditions for frozen F-theory models
  4. 6d F-theory compactifications
  5. Frozen $7$-branes
  6. F-theory constructions
  7. Frozen models via ordinary F-theory embeddings
  8. Tate forms and $(4,6)$-points
  9. Conventional embeddings of Frozen F-theory models
  10. Aspinwall-Gross model
  11. Compact $\mathbb{P}^1 \times \mathbb{P}^1$ with one frozen
  12. Compact $\mathbb{P}^1 \times \mathbb{P}^1$ with two frozen
  13. Distinguishing frozen from unfrozen supergravity theories
  14. Frozen LSTs, SCFTs and the Swampland
  15. 6d $\mathcal{N} = (1,0)$ theories
  16. ...and 11 more sections

Key Result

Lemma 4.1

Let $\Delta \subset B$ be the discriminant locus of an elliptic fibration, admitting a factorization into irreducible components with associated divisors $D_1, \ldots D_k$. Then every divisor $D_i$ satisfies the condition

Theorems & Definitions (4)

  • Claim 3.1
  • Claim 4.1
  • Lemma 4.1
  • Conjecture 5.1