1995/05/25 by D. M. McAvity, D M McAvity, H. Osborn · 316 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Boundary (topology) #Boundary conformal field theory #Conformal field theory #Conformal map #Conformal symmetry #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Neumann boundary condition #Operator (biology) #Operator product expansion #Physics #Primary field #Quantum Chromodynamics and Particle Interactions #Robin boundary condition #Scalar (mathematics) #cond-mat #hep-th
paper · pdf · doi:10.1016/0550-3213(95)00476-9
published in Nuclear Physics B 455(3), 522-576 (Elsevier BV) · Plain TeX file, 52 pages, with 1 postscript figure
arxiv created 1995/05/25 · openalex publication_date 1995/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions d. Calculations of the universal function of a conformal invariant ξ which appears in the two point function of scalar operators in conformally invariant theories with a plane boundary are undertaken to first order in the \vep=4-d expansion for the the operator ϕ2 in ϕ4 theory. The form for the associated functions of ξ for the two point functions for the basic field ϕα and the auxiliary field λ in the the N→ ∞ limit of the O(N) non linear sigma model for any d in the range 2<d<4 are also rederived. These results are obtained by integrating the two point functions over planes parallel to the boundary, defining a restricted two point function which may be obtained more simply. Assuming conformal invariance this transformation can be inverted to recover the full two point function. Consistency of the results is checked by considering the limit d→ 4 and also by analysis of the operator product expansions for ϕαϕβ and λλ. Using this method the form of the two point function for the energy momentum tensor in the conformal O(N) model with a plane boundary is also found. General results for the sum of the contributions of all derivative operators appearing in the operator product expansion, and also in a corresponding boundary operator expansion, to the two point functions are also derived making essential use of conformal invariance.