Dilatation operator in (super-)Yang–Mills theories on the light-cone Original Research Article

The gauge/string correspondence hints that the dilatation operator in gauge theories with the superconformal image symmetry should possess universal integrability properties for different image. We provide further support for this conjecture by computing a one-loop dilatation operator in all (super)symmetric Yang–Mills theories on the light-cone ranging from gluodynamics all the way to the maximally supersymmetric image theory. We demonstrate that the dilatation operator takes a remarkably simple form when realized in the space spanned by single-trace products of superfields separated by light-like distances. The latter operators serve as generating functions for Wilson operators of the maximal Lorentz spin and the scale dependence of the two are in the one-to-one correspondence with each other. In the maximally supersymmetric, image theory all nonlocal light-cone operators are built from a single CPT self-conjugated superfield while for image one has to deal with two distinct superfields and distinguish three different types of such operators. We find that for the light-cone operators built from only one species of superfields, the one-loop dilatation operator takes the same, universal form in all SYM theories and it can be mapped in the multi-color limit into a Hamiltonian of the image Heisenberg (super)spin chain of length equal to the number of superfields involved. For “mixed” light-cone operators involving both superfields the dilatation operator for image receives an additional contribution from the exchange interaction between superfields on the light-cone which breaks its integrability symmetry and creates a mass gap in the spectrum of anomalous dimensions.