Abstract
For a single free scalar field in d ≥ 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 ≥ 4 and co-dimension three defects in d ≥ 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.
Highlights
The rationale for this pattern is as follows
On the defect the local operators are organized in representations of so(p + 1, 1) × so(q), with the first factor acting as the usual conformal algebra in p dimensions and the latter as a usual global symmetry — neither of these symmetries is generated by a local current on the defect
This work contains some more general results, our main outcome is that most defects in the free scalar theory are ‘trivial’ in the sense that there is no room for any interesting dynamics on the defect: up to potentially an undetermined one-point function, all the n-point correlation functions of the bulk field φ are completely fixed
Summary
An expansion like equation (1.3) completely fixes the two-point function of the bulk field φ, but more work is required to constrain the higher-point functions: we have to learn about the defect OPE of the operators ψs(+) themselves.
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