Generalized AdS–CFT correspondence for Matrix theory in the large-N limit

Abstract

Guided by the generalized conformal symmetry, we investigate the extension of AdS-CFT correspondence to the matrix model of D-particles in the large N limit. We perform a complete harmonic analysis of the bosonic linearized fluctuations around a heavy Dparticle background in IIA supergravity in 10 dimensions and find that the spectrum precisely agrees with that of the physical operators of Matrix theory. The explicit forms of two-point functions give predictions for the large N behavior of Matrix theory with some special cutoff. We discuss the possible implications of our results for the large N dynamics of D-particles and for the Matrix-theory conjecture. We find an anomalous scaling behavior with respect to the large N limit associated to the infinite momentum limit in 11 dimensions, suggesting the existence of a screening mechanism for the transverse extension of the system.

PP-wave holography for Dp-brane backgrounds

“…The spectrum for the dimensions {∆ I } has been derived in previous works [10], by performing detailed supergravity analyses which have confirmed the above prediction. The results, ∆ I = 4ℓ I /7 + 2n − 3 (or ∆ I = 4ℓ I /7 + 2n − 3/2 for fermionic operators) with ℓ I being the angular momentum and n being non-negative integers, are consistent with the behavior of M(atrix) theory operators known approximately from one-loop analysis in [11], with some slight but puzzling corrections as discussed in [8,10]. In view of this, it seems reasonable to expect that certain appropriate extensions of the BMN correspondence exist for nonconformal case of Dp-branes.…”

“…as discussed in detail in [10] for the case of D0-branes. The affine time interval is −T ≤ τ ≤ T (with z(±T ) = 1/Λ) where…”

“…by defining the momentum operator 10) which satisfies the same reflection condition as the coordinate operator, P (τ ) † = P (−τ ).…”

“…In [10], complete spectrum of the supergravity fluctuations around the near-horizon D0-brane background has been worked out. By expanding the fields into the spherical harmonics on S 8 , and diagonalizing the linearized equations of motion, it was found that each physical mode of the bosonic fluctuations is described by the following scalar action in the (t, z) space * * :…”

“…(A.1) * * Note that the normalization of the coordinates t and z used in this paper differs from the conventional one used in [10] by dimensionful factor. The relation is (t, z)| here = q −1/2 (t, z)| conventional .…”