Finite landscape of 6d N=(1,0) supergravity

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 T ≤ 193 , and the rank of the gauge group is restricted to r(V)≤ 480 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…

• HU
  Harvard University
• NR
  National Research Foundation
• NR
  National Research Foundation of Korea

  Award: 2023R1A2C1006542
• MO
  Ministry of Science and ICT, South Korea

  Award: 2023R1A2C1006542
• SS
  Samsung Science and Technology Foundation

  Award: SSTF-BA2002-05
• S
  Samsung