Jefferson J368, 17 Oxford Street, Cambridge, Massachusetts 02138
Title: 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>>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 O(10^7) irreducible cliques from which anomaly-free theories may be easily built, and as a special case obtain a complete list of 19847 consistent theories for T=0, for which the maximal gauge group rank is 24. Modulo the new infinite families and absent simple factors, we give a complete characterization of anomaly-free theories and show that the bound T <= 273 is sharp.