Algebras, traces, and boundary correlators in N = 4 SYM

We study supersymmetric sectors at half-BPS boundaries and interfaces in the 4d N$$ \mathcal{N} $$ = 4 super Yang-Mills with the gauge group G, which are described by associative algebras equipped with twisted traces. Such data are in one-to-one correspondence with an infinite set of defect correlation functions. We identify algebras and traces for known boundary conditions. Ward identities expressing the (twisted) periodicity of the trace …