Explicit Bounds on the Spectrum of 6d N=(1,0) Supergravity

TL;DR

This paper introduces a new method to derive explicit upper bounds on the particle spectrum in six-dimensional supergravity theories, inspired by F-theory compactifications and geometric structures, with initial focus on the tensor sector.

Contribution

It presents a novel bounding strategy based on birational geometry, applicable to general supergravity theories, and provides explicit bounds on the tensor spectrum.

Findings

Derived explicit bounds on the tensor spectrum in 6d supergravity.

Connected geometric structures to physical constraints in supergravity theories.

Illustrated the bounds with an example, detailed in a companion paper.

Abstract

We propose a novel strategy to derive explicit and uniform upper bounds on the particle spectrum of six-dimensional gravitational theories with minimal supersymmetry, focusing initially on the tensor sector. The strategy is motivated by considerations of F-theory compactifications on elliptic Calabi-Yau 3-folds. However, it admits a clear bottom-up interpretation and is thus applicable to general supergravity theories modulo certain physical conjectures. At the heart of the strategy are two key structures, most natural in birational geometry: one concerns the singularity of the natural pairs on the base manifolds, and the other, the fibration generically exhibited by the bases. Put physically, the former structure keeps the effective theories from decompactifying and the latter ensures the (generic) presence of a heterotic string. We sketch our bounding strategy and present, for an illustration, the explicit bounds thereby derived on the tensor spectrum, with the technical details relegated to a companion paper [1].