Abstract
We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields. This formalism is applied to construct the defect conformal blocks for three-point functions of scalar fields. Starting from a configuration with one bulk and one defect field, for which the correlation function is determined by conformal symmetry, we explore two possibilities, adding either one additional defect or bulk field. In both cases it is possible to express the blocks in terms of classical hypergeometric functions, though the case of two bulk and one defect field requires Appell’s function F4.
Highlights
Preserve the p-dimensional subspace Rp along which the defect is localised
We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields
Starting from a configuration with one bulk and one defect field, for which the correlation function is determined by conformal symmetry, we explore two possibilities, adding either one additional defect or bulk field
Summary
We will show how conformal primary fields, both those in the bulk and the ones on the defect, can be uplifted to functions on the symmetry group Gd,p of the defect. The uplift will respect the usual action of conformal transformations on primary fields. We shall first address the defect fields for which the construction is analogous to the case of bulk fields in ordinary conformal field theory, see [22]. The rest of the section is devoted to lifting bulk primary fields to the defect conformal group. After an outline of the general strategy, we briefly recall the Iwasawa decomposition of the conformal group, which is the principal technical tool in lifting bulk fields. The lift is constructed explicitly for scalar bulk fields
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