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  • Open Access

Explicit bounds on the spectrum of 6D N=(1,0) supergravity

Caucher Birkar*

Seung-Joo Lee†

  • Yau Mathematical Sciences Center, Jingzhai, Tsinghua University, Hai Dian District, Bejing, China 100084

  • *Contact author: birkar@tsinghua.edu.cn
  • †Contact author: seungjoolee@yonsei.ac.kr
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Phys. Rev. D 113, 026006 – Published 8 January, 2026

DOI: https://doi.org/10.1103/twz8-h9dz

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 threefolds. 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 [C. Birkar and S. J. Lee, arXiv:2507.06317].

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Phys. Rev. D 113, 026006– Published 8 January, 2026
  • Received 14 October 2025
  • Accepted 2 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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