Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills

Details Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills

2010-12-17

arxiv.org/abs/1012.3983v3

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, see also overview article arXiv:1012.3982; v2: references to other chapters updated; v3: references added, typos fix

Scientific paper

In this chapter of "Review of AdS/CFT Integrability" we introduce 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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