Commuting conformal and dual conformal symmetries in the Regge limit

Abstract

In this paper we continue our study of the dual SL ( 2 , C ) symmetry of the BFKL equation, analogous to the dual conformal symmetry of N = 4 super-Yang–Mills. We find that the ordinary and dual SL ( 2 , C ) 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 N = 4 SYM, however, and one can extract a generator from the dual SL ( 2 , C ) close to the bi-local form associated with Yangian algebras. We also discuss the issue of whether the dual SL ( 2 , C ) 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 N = 4 satisfies an anomalous Ward identity. At least for the lowest orders it seems possible to recover the dual SL ( 2 , C ) by deforming its representation, keeping open the possibility that it is an exact symmetry of BFKL. Independently of a possible relation to N = 4 scattering amplitudes, this opens an avenue for explaining the integrability of BFKL in terms of two finite-dimensional subalgebras.