Towards a complete classification of 6D supergravities

Abstract

The constraints arising from anomaly cancellation are particular strong for chiral theories in six dimensions. We make progress towards a complete classification of 6D supergravities with minimal supersymmetry and non-abelian gauge group. First, we generalize a previously known infinite class of anomaly-free theories which has $T\gg 9$ to essentially any semi-simple gauge group and infinitely many choices for hypermultiplets. The construction relies on having many decoupled sectors all selected from a list of four simple theories which we identify. Second, we use ideas from graph theory to rephrase the task of finding anomaly-free theories as constructing cliques in a certain multigraph. A branch-and-bound type algorithm is described which can be used to explicitly construct, in a $T$-independent way, anomaly-free theories with an arbitrary number of simple factors in the gauge group. We implement these ideas to generate an ensemble of $\mathcal{O}(10^7)$ irreducible cliques from which anomaly-free theories may be easily built, and as a special case obtain a complete list of $19,847$ consistent theories for $T=0$, for which the maximal gauge group rank is $24$. Modulo $\mathrm{U}(1)$, $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ simple factors and the new infinite families, we give a complete characterization of anomaly-free theories and show that the bound $T\le 273$ is sharp.

40 pages + appendices, 11 figures, 1 map. v2: minor changes, clarified discussion of global anomalies. v3: JHEP version + correction to D_10 entry of table on page 28

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Cited by in corpus (3)

• Finiteness and the Emergence of Dualities
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• A new infinite class of $6d$, $\mathcal{N}=(1,0)$ supergravities