World-Sheets from Super Yang-Mills

We examine whether the free energy of N=4 super Yang-Mills theory (SYM) infour dimensions corresponds to the partition function of the AdS_5 x S^5superstring when corresponding operators are inserted into both theories. Weobtain a formal free energy of N=4 U(N) SYM in four dimensions generated by theFeynman graph expansion to all orders of the 't Hooft coupling expansion witharbitrary N. This free energy is written as the sum over discretized closedtwo-dimensional surfaces that are identified with the world-sheets of thestring. We compare this free energy with a formal partition function of thediscretized AdS_5 x S^5 superstring with the kappa-symmetry fixed in thekilling gauge and in the expansion corresponding to the weak 't Hooft couplingexpansion in the SYM. We find common properties on both sides, although furtherstudies are required to obtain a more precise comparison. Our result suggests amechanism for how the world-sheet appears dynamically from N=4 SYM, thusenabling us to derive how the AdS_5 x S^5 superstring is reproduced in theAdS/CFT correspondence.Comment: 24 pages, 7 figures, typos corrected, references adde