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

Abstract

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.

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

References in corpus (6)

• Review of AdS/CFT Integrability, Chapter VI.1: Superconformal Symmetry
• Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve
• Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the R-Matrix Formalism
• Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
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