Towards the exact dilatation operator of image super-Yang–Mills theory Original Research Article

We investigate the structure of the dilatation operator D of planar image SYM in the sector of single trace operators built out of two chiral combinations of the 6 scalars. Previous results at low orders in ʹt Hooft coupling λ suggest that D has a form of an image spin chain Hamiltonian with long range multiple spin interactions. Instead of the usual perturbative expansion in powers of λ, we split D into parts image according to the number n of independent pairwise interactions between spins at different sites. We determine the coefficients of spin–spin interaction terms in image by imposing the condition of regularity of the BMN-type scaling limit. For long spin chains, these coefficients turn out to be expressible in terms of hypergeometric functions of λ, which have regular expansions at both small and large values of λ. This suggest that anomalous dimensions of “long” operators in the two-scalar sector should generically scale as image at large λ, i.e., in the same way as energies of semiclassical states in dual image string theory.