### 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(2N) superconformal transformations. We construct the R-matrix on this space and identify the dilatation operator as the Hamiltonian of the Heisenberg SL(2N) spin chain.

Original language | English (US) |
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Pages (from-to) | 385-401 |

Number of pages | 17 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 594 |

Issue number | 3-4 |

DOIs | |

State | Published - Aug 5 2004 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*594*(3-4), 385-401. https://doi.org/10.1016/j.physletb.2004.04.092