World-Sheets from N=4 Super Yang-Mills(Particles and Fields)

概要

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We examine whether the free energy of N=4 super Yang-Mills theory (SYM) in four dimensions corresponds to the partition function of the AdS_5×S^5 superstring when the corresponding operators are inserted into both theories. We obtain the formal free energy of N=4U(N) SYM in four dimensions generated by the Feynman graph expansion to all orders of the 't Hooft coupling expansion with arbitrary N. This free energy is written as the sum over discretized closed two-dimensional surfaces that are identified with the world-sheets of the string. We compare this free energy with the formal partition function of the discretized AdS_5×S^5 superstring with the kappa-symmetry fixed in the killing gauge and in the expansion corresponding to the weak 't Hooft coupling expansion in the SYM. We find that some of their properties are identical, although further studies are required to obtain a more precise comparison. Our result suggests a mechanism thorough which the world-sheet emerges dynamically from N=4 SYM and this enables us to derive the manner in which the AdS_5×S^5 superstring is reproduced in the AdS/CFT correspondence.
2006-11-25