SciPost Submission Page
Finite Landscape of 6d N=(1,0) Supergravity
by Hee-Cheol Kim, Cumrun Vafa, Kai Xu
Submission summary
| Authors (as registered SciPost users): | Hee-Cheol Kim |
| Submission information | |
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| Preprint Link: | scipost_202512_00005v1 (pdf) |
| Date submitted: | Dec. 2, 2025, 2:23 p.m. |
| Submitted by: | Hee-Cheol Kim |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We present a bottom-up argument showing that the number of massless fields in six-dimensional quantum gravitational theories with eight supercharges is uniformly bounded. Specifically, we show that the number of tensor multiplets is bounded by $T\leq 193$, and the rank of the gauge group is restricted to $r(V)\leq 480$. Given that F-theory compactifications on elliptic CY 3-folds are a subset, this provides a bound on the Hodge numbers of elliptic CY 3-folds: $h^{1,1}({\rm CY_3})\leq 491$, $h^{1,1}({\rm Base})\leq 194$ which are saturated by special elliptic CY 3-folds. This establishes that our bounds are sharp and also provides further evidence for the string lamppost principle. These results are derived by a comprehensive examination of the boundaries of the tensor moduli branch, showing that any consistent supergravity theory with $T\neq0$ must include a BPS string in its spectrum corresponding to a "little string theory" (LST) or a critical heterotic string. From this tensor branch analysis, we establish a containment relationship between SCFTs and LSTs embedded within a gravitational theory. Combined with the classification of 6d SCFTs and LSTs, this then leads to the above bounds. Together with previous works, this establishes a bound on the number of massless fields in the supergravity for $d\geq 6$.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
1) We added a paragraph (second from the bottom) on page 4 to address the first point. This paragraph clarifies how the BPS string cone is defined and derived in a general 6D supergravity theory that may not admit a geometric or string-theoretic construction. As explained there, equation (2.1) encodes a reciprocal relation that defines both the tensor cone and the BPS string cone, given our assumption stated on the same page that the tensor moduli space is bounded by tensionless BPS string loci. It also makes explicit that the generators of the BPS cone are the charges of BPS strings that can become tensionless at some point in moduli space.
2) We revised the last sentence of the abstract.
3) We added footnote 2 on page 5.
4) We corrected the grammar issues in the introduction and in the 3rd paragraph of section 2.1.
5) We modified this accordingly.