Line and surface defects for the free scalar field

Abstract

For a single free scalar field in $d\ge 2$ dimensions, almost all the unitary conformal defects must be `trivial' in the sense that they cannot hold interesting dynamics. The only possible exceptions are monodromy defects in $d\ge 4$ and co-dimension three defects in $d\ge 5$. As an intermediate result we show that the $n$-point correlation functions of a conformal theory with a generalized free spectrum must be those of the generalized free theory.

41 pages. v3: matches journal version

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