On marginal operators in boundary conformal field theory

  • Christopher P. Herzog
  • Itamar ShamirEmail author
Open Access
Regular Article - Theoretical Physics


The presence of a boundary (or defect) in a conformal field theory allows one to generalize the notion of an exactly marginal deformation. Without a boundary, one must find an operator of protected scaling dimension ∆ equal to the space-time dimension d of the conformal field theory, while with a boundary, as long as the operator dimension is protected, one can make up for the difference d − ∆ by including a factor z−d in the deformation where z is the distance from the boundary. This coordinate dependence does not lead to a reduction in the underlying SO(d, 1) global conformal symmetry group of the boundary conformal field theory. We show that such terms can arise from boundary flows in interacting field theories. Ultimately, we would like to be able to characterize what types of boundary conformal field theories live on the orbits of such deformations. As a first step, we consider a free scalar with a conformally invariant mass term z2φ2, and a fermion with a similar mass. We find a connection to double trace deformations in the AdS/CFT literature.


Boundary Quantum Field Theory Conformal Field Theory Conformal and W Symmetry 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Mathematics DepartmentKing’s College LondonLondonU.K.
  2. 2.C.N. Yang Institute for Theoretical Physics, Department of Physics and AstronomyStony Brook UniversityStony BrookU.S.A.
  3. 3.SISSA and INFNTriesteItaly

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