期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 1, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP01(2018)013
关键词
AdS-CFT Correspondence; Conformal Field Theory
资金
- JSPS [15K17628, 16H02182]
- JSPS
- Program for Leading Graduate Schools, MEXT, Japan
- World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan
- Grants-in-Aid for Scientific Research [16H02182, 15K17628, 17J02745] Funding Source: KAKEN
We study the operator product expansion (OPE) for scalar conformal defects of any codimension in CFT. The OPE for defects is decomposed into \ defect OPE blocks, the irreducible representations of the conformal group, each of which packages the contribution from a primary operator and its descendants. We use the shadow formalism to deduce an integral representation of the defect OPE blocks. They are shown to obey a set of constraint equations that can be regarded as equations of motion for a scalar field propagating on the moduli space of the defects. By employing the Radon transform between the AdS space and the moduli space, we obtain a formula of constructing an AdS scalar fi eld from the defect OPE block for a conformal defect of any codimension in a scalar representation of the conformal group, which turns out to be the Euclidean version of the HKLL formula. We also introduce a duality between conformal defects of different codimensions and prove the equivalence between the defect OPE block for codimension-two defects and the OPE block for a pair of local operators.
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