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 ≫ 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 \( \mathcal{O} \)(107) 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 U(1), SU(2) and SU(3) simple factors and the new infinite families, we give a complete characterization of anomaly-free theories and show that the bound 𝑇 ≤ 273 is sharp.
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Acknowledgments
We thank Hee-Cheol Kim for insightful discussions, both Hee-Cheol Kim and Gary Shiu for comments on an earlier draft, and the 2023 Summer Program of the Simons Center for Geometry and Physics for their kind hospitality. The work of Y.H. and G.L. is supported in part by MEXT Leading Initiative for Excellent Young Researchers Grant Number JPMXS0320210099.
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Hamada, Y., Loges, G.J. Towards a complete classification of 6D supergravities. J. High Energ. Phys. 2024, 95 (2024). https://doi.org/10.1007/JHEP02(2024)095
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DOI: https://doi.org/10.1007/JHEP02(2024)095