Abstract
In this paper we study the constraints imposed by conformal invariance on extended objects a.k.a. defects in a conformal field theory. We identify a particularly nice class of defects that is closed under conformal transformations. Correlation function of the defect with a bulk local operator is fixed by conformal invariance up to an overall constant. This gives rise to the notion of defect expansion, where the defect itself is expanded in terms of local operators. This expansion generalizes the idea of the boundary state. We will show how one can fix the correlation function of two defects from the knowledge of the defect expansion. The defect correlator admits a number of conformal cross-ratios depending on their dimensionality. We find the differential equation obeyed by the conformal block and solve them in certain special cases.
Highlights
There has been a significant amount of work on BPS defect operators in supersymmetric conformal field theories
In this paper we study the constraints imposed by conformal invariance on extended objects a.k.a. defects in a conformal field theory
We show that their two point function is fixed by conformal symmetry modulo defect expansion coefficients, just as in the case of local operators
Summary
The conformal symmetry group is a group of transformations that keeps all the angles fixed. We take the action special conformal transformations to be vanishing and label the representation of the local operator by scaling dimension and spin. The defect theory is different from the usual conformal field theory in one crucial aspect: it does not have a stress tensor This is to be expected because the defect system freely exchanges energy with the bulk. This is used to define a sort of operator product expansion in which the spherical defect is expanded in terms of bulk-local operators.
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