Spin chain sigma models with fermions
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2004
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Int School Advanced Studies
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Abstract
The complete one-loop planar dilatation operator of N = 4 supersymmetric Yang-Mills is isomorphic to the hamiltonian of an integrable PSU(2 , 2|4) quantum spin chain. We construct the non-linear sigma models describing the continuum limit of the SU(1|3) and SU(2|3) sectors of the complete N = 4 chain. We explicitely identify the spin chain sigma model with the one for a superstring moving in AdS 5 × S 5 with large angular momentum along the five-sphere.
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© SISSA/ISAS 2004. It is a pleasure to thank E. Álvarez, C. Gómez, K. Landsteiner and T. Ortín for useful discussions. R.H. acknowledges the financial support provided through the European Community’s Human Potential Programme under contract HPRN-CT-2000-00131 “Quantum Structure of Space-time”, the Swiss Office for Education and Science and the Swiss National Science Foundation. The work of E.L. was supported by a Ramón y Cajal contract of the MCYT and in part by the Spanish DGI under contract FPA2003-04597.