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Quantum integrability in (super) Yang-Mills theory on the light-cone

A. V. Belitsky·S. E. Derkachov·G. P. Korchemsky·A. N. Manashov
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Abstract

We employ the light-cone formalism to construct in the (super) Yang-Mills theories in the multi-color limit the one-loop dilatation operator acting on single trace products of chiral superfields separated by light-like distances. In the N=4 Yang-Mills theory it exhausts all Wilson operators of the maximal Lorentz spin while in nonsupersymmetric Yang-Mills theory it is restricted to the sector of maximal helicity gluonic operators. We show that the dilatation operator in all N-extended super Yang-Mills theories is given by the same integral operator which acts on the (N+1)-dimensional superspace and is invariant under the SL(2|N) superconformal transformations. We construct the R-matrix on this space and identify the dilatation operator as the Hamiltonian of the Heisenberg SL(2|N) spin chain.

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A. V. Belitsky, S. E. Derkachov, G. P. Korchemsky, A. N. Manashov. 2004-12-27. Quantum integrability in (super) Yang-Mills theory on the light-cone. https://doi.org/10.1016/j.physletb.2004.04.092

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