A bound on 6D N=1 supergravities
Vijay Kumar, Washington Taylor
TL;DR
The article addresses whether six-dimensional chiral (1,0) supergravity theories with one tensor multiplet and no U(1) factors can host infinitely many distinct gauge groups and matter representations under anomaly cancellation with positive gauge-kinetic terms. By analyzing the anomaly polynomial $I$ and its Green-Schwarz factorization, together with the gravitational bound $n_h-n_v=244$, the authors perform a case-based finiteness proof: any infinite family would either require unbounded ranks or unbounded numbers of factors, both of which lead to incompatible matter content or divergent contributions to $n_h-n_v$. Consequently, the set of admissible semi-simple gauge groups and matter representations is finite under the stated assumptions, and the paper outlines a pathway toward a systematic block-based classification. The work connects to string theory via potential realizations in F-theory and Calabi–Yau compactifications, discusses extensions to more tensor multiplets and Abelian factors, and highlights implications for the 6D landscape and swampland program.
Abstract
We prove that there are only finitely many distinct semi-simple gauge groups and matter representations possible in consistent 6D chiral (1,0) supergravity theories with one tensor multiplet. The proof relies only on features of the low-energy theory; the consistency conditions we impose are that anomalies should be cancelled by the Green-Schwarz mechanism, and that the kinetic terms for all fields should be positive in some region of moduli space. This result does not apply to the case of the non-chiral (1,1) supergravities, which are not constrained by anomaly cancellation.