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For the purpose of better understanding the AdS/CFT correspondence it isuseful to have a description of the theory for all values of the 't Hooftcoupling, and for all $N$. We discuss such a description in the framework ofMatrix theory for SYM on D4-branes, which is given in terms of quantummechanics on the moduli space of solutions of the Nahm equations. Thisdescription reduces to both SYM perturbation theory and to closed stringperturbation theory, each in its appropriate regime of validity, suggesting away of directly relating the variables in the two descriptions. For example, itshows explicitly how holes in the world-sheets of the 't Hooft expansion closeto give closed surfaces.Comment: 19 page

From SYM perturbation theory to closed strings in matrix theory