Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-07-11
Nucl.Phys. B572 (2000) 651-669
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, LaTeX, minor errors corrected, Conclusions and one reference added, final version to be published in Nucl. Phys. B
Scientific paper
10.1016/S0550-3213(99)00833-0
We consider the role of boundary conditions in the $AdS_{d+1}/CFT_{d}$ 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 $\frac{d}{2}$. 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 $-d^2/4
Minces Pablo
Rivelles Victor O.
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