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Abstract: Superconformal field theories in d<5 permit rich families of boundary conditions, junctions, and interfaces which may be used to engineer new conformal field theories and explore non-perturbative phenomena. Many of these properties descend from the existence of a 6d (2,0) SCFT on the worldvolume of M5 branes, but this theory permits no Lagrangian description, making it difficult to study directly. Two closely related proposals to understand the 6d theory involve either boosting the M-theory system into the infinite momentum frame, leading to a matrix model description in terms of 5d instanton particles; alternatively, one can compactify the 6d theory on a Lorentzian/null circle, leading to an exotic non-Lorentzian yet Lagrangian 5d SCFT.
In this talk, I present ongoing work joint with Mykola Dedushenko on superconformal initial conditions for the null 5d SCFT, which are natural lightcone analogs of boundary conditions. These initial conditions may be thought of as protected field theory states arising from QFT on the Lorentzian half-space, and we find both Dirichlet and Neumann conditions which preserve an unusual amount of supersymmetry. Some comparisons with the matrix description can be made, but the field theory viewpoint may prove to be a more general and direct approach. Given this is in-progress work in a slightly exotic setting, I will encourage discussion and suggestions for how to expand on this proposal.