Are M-atrix theory and Maldacena’s conjecture related?

We give arguments in the support of a relation between M-atrix theory and Maldacena’s conjecture. In the limit when the light-like circle of M-theory decompactifies, M-atrix theory conjecture implies the equivalence of 11-D light-cone supergravity and stronglycoupled (0+1)-D SYM. The large-N version of Maldacena’s conjecture, SUGRA/SYM duality, can be formulated as the validity of supergravity description in the substringy region with some restrictions on the curvature, etc. It implies, in the one dimensional SYM case, the equivalence between strongly-coupled (0+1)-D SYM and 11-D supergravity compactified on a spatial circle in the formal Sen-Seiberg limit. On the other hand, there is a classical equivalence between 11-D supergravity on a light-like circle and on a spatial circle in the formal Sen-Seiberg limit. We thus see that in the (0+1)-D SYM case, the large-N, low energy version of M-atrix theory is equivalent to SUGRA/SYM duality. ∗ E-mail: [email protected] M-atrix theory [1, 2] and Maldacena’s conjecture [3] are similar in the sense that both are about the equivalence between M/string theories (i.e. theories in the bulk space-time) and brane world-volume theories. But does this similarity go beyond a mere analogy? Maldacena’s conjecture relates M/string theory on a curved background to SYM in the flat space, whereas M-atrix theory relates M-theory on a transverse torus to SYM on a dual torus. For example, consider finite-N M-atrix theory on a 3-torus. If V3 is the volume of M-theory transverse 3-torus and R–the radius of light-like circle, then the corresponding D=4 SYM is defined on a dual 3-torus of volume Ṽ3 = (RM 3 P ) V −1 3 . Dual 3-torus decompactifies in the limit V3 → 0 , but g YM = (M PV3) also blows up in this limit. In the large-N limit one has to take R → ∞. We thus have g YM ≫ 1 and N ≫ 1, and this limit is different from the one involved in AdS5/CFT4 correspondence. '