Holographic reformulation of string theory on AdS5×S5 background in the PP-wave limit

Abstract

The recent proposal on the correspondence between the N = 4 super Yang-Mills theory and string theory in the Penrose limit of the AdS 5 ×S 5 geometry involves a few puzzles from the viewpoint of holographic principle, especially in connection with the interpretation of times. To resolve these puzzles, we propose to interpret the PP-wave strings on the basis of tunneling null geodesics connecting boundaries of the AdS geometry.Our approach predicts a direct and systematic identification of the S-matrix of Euclidean string theory in the bulk with the short-distance structure of correlation functions of super Yang-Mills theory on the AdS boundary, as an extension of the ordinary relation in supergravity-CFT correspondence. Holography requires an infinite number of contact terms for interaction vertices of string field theory and constrains their forms in a way consistent with supersymmetry.

PP-wave holography for Dp-brane backgrounds

“…As discussed in [12] in the WKB approximation, inclusion of linearized fluctuations leads to the shift J → J + 4, which is appropriate for a scalar operator, whose origin in the present context is the zero-point energies, 4 = 8 × 1/2, of 8 transverse directions in the 10D space-time.…”

“…[12] [13] for the case of D3-branes, which allows us to avoid singularities at the horizon for nonconformal Dp-branes and to establish a direct connection between bulk and boundary.…”

On the propagator of a scalar field in AdS × S and in its plane wave limit

“…The above solution can indeed be obtained from (14) by taking the sum of the expressions for ∆ + and ∆ − . In addition one finds another simple structure by taking the difference.…”

“…In this Section we will use the propagator on pure AdS d+1 given by (14) and the spherical harmonics on S d ′ +1 to construct the propagator on AdS d+1 ×S d ′ +1 via its mode expansion, summing up all the KK modes. We will be able to perform the sum only for special mass values where the conformal dimensions ∆ ± of the scalar modes are linear functions of l, with l denoting the lth mode in the KK tower.…”

“…One of the crucial unsolved questions in this setting concerns the issue of holography [10][11][12][13][14]. In the Penrose limiting process the old 4-dimensional conformal boundary is put beyond the new plane wave space, which by itself has a one-dimensional conformal boundary.…”