Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 4, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP04(2016)091
Keywords
Boundary Quantum Field Theory; Conformal and W Symmetry; Field Theories in Higher Dimensions; Space-Time Symmetries
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Funding
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research Innovation
- Compagnia di San Paolo contract MAST: Modern Applications of String Theory [TO-Call3-2012-0088]
- COST Action MP1210 The String Theory Universe
- Interuniversity Attraction Poles Programme - Belgian Science Policy [P7/37]
- European Research Council [ERC-2013-CoG 616732 HoloQosmos]
- National Science Foundation of Belgium (FWO) [G.001.12, G.0.E52.14N]
- FAPESP grant [2015/14796-7, CERN/FIS-NUC/0045/2015]
- Foundation for Science and Technology of Portugal (FCT)
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We discuss consequences of the breaking of conformal symmetry by a flat or spherical extended operator. We adapt the embedding formalism to the study of correlation functions of symmetric traceless tensors in the presence of the defect. Two-point functions of a bulk and a defect primary are fixed by conformal invariance up to a set of OPE coefficients, and we identify the allowed tensor structures. A correlator of two bulk primaries depends on two cross-ratios, and we study its conformal block decomposition in the case of external scalars. The Casimir equation in the defect channel reduces to a hypergeometric equation, while the bulk channel blocks are recursively determined in the light-cone limit. In the special case of a defect of codimension two, we map the Casimir equation in the bulk channel to the one of a four-point function without defect. Finally, we analyze the contact terms of the stress-tensor with the extended operator, and we deduce constraints on the CFT data. In two dimensions, we relate the displacement operator, which appears among the contact terms, to the reflection coefficient of a conformal interface, and we find unitarity bounds for the latter.
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