Commuting conformal and dual conformal symmetries in the Regge limit Original Research Article

In this paper we continue our study of the dual image symmetry of the BFKL equation, analogous to the dual conformal symmetry of image super-Yang–Mills. We find that the ordinary and dual image symmetries do not generate a Yangian, in contrast to the ordinary and dual conformal symmetries in the four-dimensional gauge theory. The algebraic structure is still reminiscent of that of image SYM, however, and one can extract a generator from the dual image close to the bi-local form associated with Yangian algebras. We also discuss the issue of whether the dual image symmetry, which in its original form is broken by IR effects, is broken in a controlled way, similar to the way the dual conformal symmetry of image satisfies an anomalous Ward identity. At least for the lowest orders it seems possible to recover the dual image by deforming its representation, keeping open the possibility that it is an exact symmetry of BFKL. Independently of a possible relation to image scattering amplitudes, this opens an avenue for explaining the integrability of BFKL in terms of two finite-dimensional subalgebras.