Generalized Conformal Symmetry and Oblique AdS/CFT Correspondence for Matrix Theory

The large N behavior of Matrix theory is discussed on the basis of the previously proposed generalized conformal symmetry. The concept of ‘oblique’ AdS/CFT correspondence, in which the conformal symmetry involves both the spacetime coordinates and the string coupling constant, is proposed. Based on the explicit predictions for two-point correlators, possible implications for the Matrix-theory conjecture are discussed. PACS numbers: 11.25.-w, 04.60.-m The Matrix-theory conjecture [1] requires us to investigate the dynamics of D-particles described by the supersymmetric Yang-Mills matrix quantum mechanics in the large N limit. Unfortunately, very little is known as for the relevant large N behaviors of the matrix quantum mechanics. In the present talk, I shall discuss the large N limit of Matrix theory by extending the AdS/CFT correspondence to the matrix quantum mechanics using the previously proposed generalized conformal symmetry as a guide. The paper is organized into three parts. In the first part, I begin by briefly recalling the Matrix-theory conjecture and review the so-called DLCQ interpretation at finite N . The latter interpretation will be used as an intermediate step for our later arguments. Then in the second part, after a brief discussion on the generalized conformal symmetry [2, 3] from the point of view of the AdS/CFT correspondence, I introduce the notion of ‘oblique’ AdS/CFT correspondence for nonconformal D0-branes. In the third part, I discuss the results of the harmonic analysis of supergravity fluctuations around the Dparticle background and its predictions for the two-point corrrelators of Matrix theory operators in the large N limit, based on our recent work [4] which contains, to my knowledge, the first extensive computation of the correlators for dilatonic case based on the AdS/CFT correspondence. I then propose to interpret the anomalous large N scaling behavior found from this analysis as an indication of a screening mechanism which may reconcile the holographic growth of the transverse size with 11 dimensional boost invariance. ‡ e-mail address: [email protected] Generalized Conformal Symmetry and Oblique AdS/CFT Correspondence . . . 2 1. Matrix-theory conjecture and the DLCQ interpretation The basic assumption of Matrix theory [1] is that the low-energy effective super YangMills theory of D-particles in type IIA superstring theory is the exact description of ‘M-theory’ in the infinite-momentum limit where the total 11th dimensional momentum P10 becomes infinite: P10 = N/R →∞, (1.1) where R = gs`s is the radius of the 11th dimension, which is compactified to a circle, and N is the number of D-particles. The D-particles are now interpreted as partons as the basic constituents of M-theory. The effective action is S = ∫ dt Tr ( 1 2gs`s DtXiDtXi + iθDtθ + 1 4gs`s [Xi, Xj] 2 − ....). (1.2) In the infinite-momentum limit, the 11th momentum and the Hamiltonian can be identified with the light-like momentum and the light-like Hamiltonian, respectively. P10 → P− = N/R, , H → P = −2P− = R Tr h = N