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Global aspects of the space of 6D N = 1 supergravities

Vijay Kumar, David R. Morrison, Washington Taylor

Abstract

We perform a global analysis of the space of consistent 6D quantum gravity theories with N = 1 supersymmetry, including models with multiple tensor multiplets. We prove that for theories with fewer than T = 9 tensor multiplets, a finite number of distinct gauge groups and matter content are possible. We find infinite families of field combinations satisfying anomaly cancellation and admitting physical gauge kinetic terms for T > 8. We find an integral lattice associated with each apparently-consistent supergravity theory; this lattice is determined by the form of the anomaly polynomial. For models which can be realized in F-theory, this anomaly lattice is related to the intersection form on the base of the F-theory elliptic fibration. The condition that a supergravity model have an F-theory realization imposes constraints which can be expressed in terms of this lattice. The analysis of models which satisfy known low-energy consistency conditions and yet violate F-theory constraints suggests possible novel constraints on low-energy supergravity theories.

Global aspects of the space of 6D N = 1 supergravities

Abstract

We perform a global analysis of the space of consistent 6D quantum gravity theories with N = 1 supersymmetry, including models with multiple tensor multiplets. We prove that for theories with fewer than T = 9 tensor multiplets, a finite number of distinct gauge groups and matter content are possible. We find infinite families of field combinations satisfying anomaly cancellation and admitting physical gauge kinetic terms for T > 8. We find an integral lattice associated with each apparently-consistent supergravity theory; this lattice is determined by the form of the anomaly polynomial. For models which can be realized in F-theory, this anomaly lattice is related to the intersection form on the base of the F-theory elliptic fibration. The condition that a supergravity model have an F-theory realization imposes constraints which can be expressed in terms of this lattice. The analysis of models which satisfy known low-energy consistency conditions and yet violate F-theory constraints suggests possible novel constraints on low-energy supergravity theories.

Paper Structure

This paper contains 23 sections, 77 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Anomalies and lattices
  3. Anomaly cancellation
  4. Proof of integrality
  5. Integral lattices and dyonic strings
  6. Finite bound for fixed $T < 9$
  7. Infinite families for $T \geq 9$
  8. Example: Infinite families at fixed $T \geq 9$
  9. Example: Infinite families with unbounded numbers of factors
  10. Supergravity models in F-theory
  11. Mapping to F-theory
  12. F-theory constraints on low-energy supergravity
  13. Examples
  14. Examples with F-theory realizations: $SU(N)$ product models at $T = 1$
  15. Example: Embedding failure
  16. ...and 8 more sections

Figures (1)

  • Figure 1: Kähler cone for the one point blowup of $\mathbb{F}_1$ away from $D_v$.