The spin chain analogy of the problem of computing conformal dimensions of compostie operators in N=4 super Yang-Mills theory and the idea that the theory and its string dual could be integrable and could perhaps be solved by a Bethe ansatz has attracted a lot of attention. The present view is that this should be done in two steps. First one must solve the asymptotic Bethe ansatz which should obtain the spectrum of infinitely large operators where the problem simplifies considerably, being posed as scattering of magnons with a factorized S-matrix. Subsequently a thermodynamic Bethe ansatz should be used to find the spectrum of finite size operators. An interesting window onto finite size effects is the giant magnon, the string dual of the spin chain magnon. The seminar will discuss the giant magnon solution of string theory and attempts to interpret its finite size effects as the spectrum of a single magnon on an orbifolded version of N=4 Yang-Mills theory with reduced supersymmetry.

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