Conformal field theories near a boundary in general dimensions
Abstract
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 twopoint function of scalar operators in conformally invariant theories with a plane boundary are undertaken to first order in the ge = 4  d expansion for the operator φ^{2} in φ^{4} theory. The form for the associated functions of ξ for the twopoint functions for the basic field φ^{α} and the auxiliary field λ in the N → ∞ limit of the O( N) nonlinear sigma model for any d in the range 2 < d < 4 are also rederived. These results are obtained by integrating the twopoint functions over planes parallel to the boundary, defining a restricted twopoint function which may be obtained more simply. Assuming conformal invariance this transformation can be inverted to recover the full twopoint function. Consistency of the results is checked by considering the limit d → 4 and also by analysis of the operator product expansions for φ^{α}φ^{β} and λλ. Using this method the form of the twopoint function for the energymomentum 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 twopoint functions are also derived making essential use of conformal invariance.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1995
 DOI:
 10.1016/05503213(95)004769
 arXiv:
 arXiv:condmat/9505127
 Bibcode:
 1995NuPhB.455..522M
 Keywords:

 Condensed Matter;
 High Energy Physics  Theory
 EPrint:
 Plain TeX file, 52 pages, with 1 postscript figure