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

TL;DR

This paper uses light-cone formalism to construct the one-loop dilatation operator in (super) Yang-Mills theories, revealing its integrable spin chain structure and superconformal symmetry properties.

Contribution

It demonstrates that the dilatation operator in all N-extended super Yang-Mills theories is represented by a universal integral operator with SL(2|N) symmetry, linked to a spin chain Hamiltonian.

Findings

The dilatation operator acts on superspace with SL(2|N) invariance.

In N=4 theory, it accounts for all maximal spin Wilson operators.

In nonsupersymmetric case, it focuses on maximal helicity gluonic operators.

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.