Matrix theory, AdS/CFT, and gauge/gravity correspondence
Summary: With \(N\to\infty\) being fixed, \(R\to\infty\), 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 \(S_{\mathrm{eff}}(R,F)\), 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 \(\Gamma(Y)\) for the arbitrary matrix configuration \(Y\). \(\Gamma(Y)\) is \(R\) and thus \(p^+\) independent. If \(W(R,F)=S_{\mathrm{eff}}(R,F)\), \(\Gamma(Y)\) 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 \(\text{SYM}_{4}\) with the \(4d\) background field \(F_0\), we give a possible way to induce the radial dependent \(5d\) field \(F(\sigma)\).
scientific article; zbMATH DE number 6530698
scientific article