TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.20.1.016
TI  - Finite landscape of 6d N=(1,0) supergravity
PY  - 2026/01/21
UR  - https://scipost.org/SciPostPhys.20.1.016
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 20
IS  - 1
SP  - 016
A1  - Kim, Hee-Cheol
AU  - Vafa, Cumrun
AU  - Xu, Kai
AB  - 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 $T≤ 193$, and the rank of the gauge group is restricted to $r(V)≤ 480$. 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: $h^{1,1}({\rm CY_3})≤ 491$, $h^{1,1}({\rm Base})≤ 194$ 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 $T≠0$ 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 $d≥ 6$.
ER  -

@Article{10.21468/SciPostPhys.20.1.016,
	title={{Finite landscape of 6d N=(1,0) supergravity}},
	author={Hee-Cheol Kim and Cumrun Vafa and Kai Xu},
	journal={SciPost Phys.},
	volume={20},
	pages={016},
	year={2026},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.20.1.016},
	url={https://scipost.org/10.21468/SciPostPhys.20.1.016},
}