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 coef- ficients, 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.

Defects in conformal field theory

BILLO', Marco;Meineri, Marco
2016-01-01

Abstract

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 coef- ficients, 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.
2016
2016
4
1
55
http://link.springer.com/journal/13130
Boundary Quantum Field Theory; Conformal and W Symmetry; Field Theories in Higher Dimensions; Space-Time Symmetries; Nuclear and High Energy Physics
Billo', Marco; Gonçalves, Vasco; Lauria, Edoardo; Meineri, Marco
File in questo prodotto:
File Dimensione Formato  
art%3A10.1007%2FJHEP04%282016%29091.pdf

Accesso aperto

Descrizione: Articolo principale
Tipo di file: PDF EDITORIALE
Dimensione 967.27 kB
Formato Adobe PDF
967.27 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1602991
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 185
  • ???jsp.display-item.citation.isi??? 173
social impact