Scalar field theory in the AdS / CFT correspondence revisited

Jul, 1999
20 pages
Published in:
  • Nucl.Phys.B 572 (2000) 651-669
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Abstract:
We consider the role of boundary conditions in the AdSd+1/CFTdAdS_{d+1}/CFT_{d} correspondence for the scalar field theory. Also a careful analysis of some limiting cases is presented. We study three possible types of boundary conditions, Dirichlet, Neumann and mixed. We compute the two-point functions of the conformal operators on the boundary for each type of boundary condition. We show how particular choices of the mass require different treatments. In the Dirichlet case we find that there is no double zero in the two-point function of the operator with conformal dimension d2\frac{d}{2}. The Neumann case leads to new normalizations for the boundary two-point functions. In the massless case we show that the conformal dimension of the boundary conformal operator is precisely the unitarity bound for scalar operators. We find a one-parameter family of boundary conditions in the mixed case. There are again new normalizations for the boundary two-point functions. For a particular choice of the mixed boundary condition and with the mass squared in the range d2/4<m2<d2/4+1-d^2/4<m^2<-d^2/4+1 the boundary operator has conformal dimension comprised in the interval [d22,d2][\frac{d-2}{2}, \frac{d}{2}]. For mass squared m2>d2/4+1m^2>-d^2/4+1 the same choice of mixed boundary condition leads to a boundary operator whose conformal dimension is the unitarity bound.
  • 11.10.Kk
  • 11.25.Mf
  • AdS/CFT correspondence
  • Boundary conditions
  • Holographic principle
  • space-time: anti-de Sitter
  • field theory: conformal
  • field theory: scalar
  • boundary condition
  • two-point function