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Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in \({\mathcal{N}=4}\) Super Yang-Mills

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Abstract

In this chapter of Review of AdS/CFT Integrability we introduce \({\mathcal{N}=4}\) Super Yang-Mills. We discuss the global superalagebra PSU(2, 2|4) and its action on gauge invariant operators. We then discuss the computation of the correlators of certain gauge invariant operators, the so-called single trace operators in the large N limit. We show that interactions in the gauge theory lead to mixing of the operators. We compute this mixing at the one-loop level and show that the problem maps to a one-dimensional spin chain with nearest neighbor interactions. For operators in the SU(2) sector we show that the spin chain is the ferromagnetic Heisenberg spin chain whose eigenvalues are determined by the Bethe equations.

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  1. Department of Physics and Astronomy, Uppsala University, 751 20, Uppsala, Sweden

    Joseph A. Minahan

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Minahan, J.A. Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in \({\mathcal{N}=4}\) Super Yang-Mills. Lett Math Phys 99, 33–58 (2012). https://doi.org/10.1007/s11005-011-0522-9

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