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The Z2 orbifold of N=4 SYM can be connected to N=2 superconformal QCD by a marginal deformation. The spin chains in this marginal family of theories have sufficient symmetry that allows for an all-loop determination of dispersion relation of BMN magnons. The exact two body S matrix is also fixed up to an overall phase. The exact dispersion relation of the magnon can be obtained from the matrix model of lowest modes on S^3, as well. I'll also talk briefly about some progress made towards the string dual of N=2 superconformal QCD, the endpoint of the deformation.

Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. But what is their physical origin? In this talk, I show how it is possible to trace the complex nature of the quantum formalism directly to the basic symmetries associated with the basic operations which allow elementary experiments to be combined into more elaborate ones. In particular, I show that, by harnessing these symmetries, the Feynman rules of quantum theory can be derived from the assumption that a pair of real numbers is associated to each sequence of measurement outcomes, and that the probability of this sequence is a real-valued function of this number pair. The derivation has numerous intriguing implications, such as pointing to a deep connection between the foundations of quantum theory and the foundations of number systems. It also demonstrates that, contrary to the rather prevalent working hypothesis that the structure of the quantum formalism has something essentially to do with nonlocality, the core of the quantum formalism in fact does not depend in any essential way on the properties of space. Reference: "Origin of Complex Quantum Amplitudes and Feynman's Rules", Phys. Rev. A 81, 022109 (2010). Full text available at www.philipgoyal.org