Defects in conformal field theory

  • Marco Billò
  • Vasco Gonçalves
  • Edoardo Lauria
  • Marco MeineriEmail author
Open Access
Regular Article - Theoretical Physics


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.


Boundary Quantum Field Theory Conformal and W Symmetry Field Theories in Higher Dimensions Space-Time Symmetries 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Marco Billò
    • 1
  • Vasco Gonçalves
    • 2
    • 3
  • Edoardo Lauria
    • 4
  • Marco Meineri
    • 5
    • 6
    Email author
  1. 1.Dipartimento di FisicaUniversità di Torino, and Istituto Nazionale di Fisica Nucleare - sezione di TorinoTorinoItaly
  2. 2.Centro de Física do Porto, Departamento de Física e Astronomia Faculdade de Ciências da Universidade do PortoPortoPortugall
  3. 3.ICTP South American Institute for Fundamental Research Instituto de Física Teórica, UNESP - Univ. Estadual PaulistaSão PauloBrasil
  4. 4.Institute for Theoretical PhysicsKU LeuvenLeuvenBelgium
  5. 5.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  6. 6.Scuola Normale Superiore, and Istituto Nazionale di Fisica Nucleare - sezione di PisaPisaItaly

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