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Résumé |
Conformal field theories, and their deformations, provide an avenue to explore the richness of quantum field
theory beyond the limited realm of perturbation theory around free fields. Supersymmetry allows for
additional insights, including some exact results. This talk will be based on a series of papers done in
collaboration with Cordova and Dumitrescu, including some work in progress. We explore and classify the
possible multiplets of operators of all possible unitary superconformal field theories above two dimensions,
and also their supersymmetry-preserving deformations. The zoo of multiplets contains some oddities,
particularly in three and four dimensions. We show that unitary superconformal field theories with more than
sixteen supercharges can exist only in three dimensions, and there only as free fields. We find that various
possible free-field representations of the conformal group cannot exist in unitary superconformal field
theories. We use this to show that mixed gauge / global anomalies cannot occur in SCFTs, though they exist
in some non-conformal QFTs. For 6d SCFTs, we find an exact relation between the conformal a-anomaly and
’t Hooft anomalies for the superconformal R-symmetry, and prove that it satisfies the a-theorem for tensor-
branch deformations. The absence of mixed anomalies ensures positivity of the a-anomaly for 6d SCFTs built
from gauge, hyper, and tensor multiplets. Aspects of Higgs branch deformations of such theories will also be
discussed. |
