Large spin corrections in image SYM image: Still a linear integral equation Original Research Article

Anomalous dimension and higher conserved charges in the image sector of image SYM for generic spin s and twist L are described by using a novel kind of non-linear integral equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-linear (finite range) integral terms, appearing in the NLIE and in the dimension formula, go to zero as image. Therefore they can be neglected at least up to the image order, thus implying a linear integral equation (LIE) and a linear dimension/charge formula respectively, likewise the ‘thermodynamic’ (i.e. infinite spin) case. Importantly, these non-linear terms go faster than any inverse logarithm power image, image, thus extending the linearity validity.