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Representation theory of super Yang-Mills algebras
We study in this article the representation theory of a family of super
algebras, called the \emph{super Yang-Mills algebras}, by exploiting the
Kirillov orbit method \textit{\`a la Dixmier} for nilpotent super Lie algebras.
These super algebras are a generalization of the so-called \emph{Yang-Mills
algebras}, introduced by A. Connes and M. Dubois-Violette in \cite{CD02}, but
in fact they appear as a "background independent" formulation of supersymmetric
gauge theory considered in physics, in a similar way as Yang-Mills algebras do
the same for the usual gauge theory. Our main result states that, under certain
hypotheses, all Clifford-Weyl super algebras \Cliff_{q}(k) \otimes A_{p}(k),
for , or and , appear as a quotient of all super
Yang-Mills algebras, for and . This provides thus a family
of representations of the super Yang-Mills algebras
Radial coordinates for defect CFTs
We study the two-point function of local operators in the presence of a
defect in a generic conformal field theory. We define two pairs of cross
ratios, which are convenient in the analysis of the OPE in the bulk and defect
channel respectively. The new coordinates have a simple geometric
interpretation, which can be exploited to efficiently compute conformal blocks
in a power expansion. We illustrate this fact in the case of scalar external
operators. We also elucidate the convergence properties of the bulk and defect
OPE decompositions of the two-point function. In particular, we remark that the
expansion of the two-point function in powers of the new cross ratios converges
everywhere, a property not shared by the cross ratios customarily used in
defect CFT. We comment on the crucial relevance of this fact for the numerical
bootstrap.Comment: Matches journal version; the attached mathematica file (Bulk CB.nb +
rec.txt) computes the conformal blocks in the bulk channe
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