Matrix Theory, AdS/CFT, and Gauge/Gravity Correspondence

Abstract

With N→∞ being fixed, R→∞, the free energy of the Matrix theory on a supergravity background F is a functional of F, W=W(R,F). We try to relate this functional with Seff(R,F), the effective action of F, where F is translation invariant along x-. The vertex function is then associated with the connected correlation function of the current densities. From W(R,F), one can construct an effective action Γ(Y) for the arbitrary matrix configuration Y. Γ(Y) is R, and thus p+ independent. If W(R,F)=Seff(R,F), Γ(Y) will give the supergravity interactions among M theory objects with no light-cone momentum exchange. We then discuss the Matrix theory dual of the 11d background generated by branes with the definite p+ as well as the gauge theory dual of the 10d background arising from the x- reduction. Finally, for SYM4 with the 4d background field F0, we give a possible way to induce the radial dependent 5d field F(σ).