A finite 6d supergravity landscape from anomalies

Abstract

6d supergravities with non-abelian gauge group are subject to many consistency conditions. While the absence of local gauge and gravitational anomalies allows for infinitely many models, we show that those conditions stemming from the absence of both local and global anomalies together are strong enough to leave only finitely many consistent models. To do this we distill the consequences of anomaly cancellation into a high-dimensional linear program whose dual can be efficiently studied using standard techniques. We obtain a universal bound on the number of tensor multiplets $T \leq 11 \cdot 273 = 3003$ and show that this leads to a finite landscape of consistent non-abelian models. Interestingly, the model which saturates this bound has gauge group $[E_8 \times F_4 \times (G_2 \times \mathrm{SU}(2))^2]^{273}$, which bears a striking resemblance to the model which saturates the bound $T \leq 193$ for F-theory constructions.