Commuting Conformal and Dual Conformal Symmetries in the Regge limit

TL;DR

This paper investigates the dual SL(2,C) symmetry of the BFKL equation in the Regge limit, comparing it to known symmetries in N=4 SYM, and explores its algebraic structure and potential exactness.

Contribution

It reveals that the dual SL(2,C) symmetry does not form a Yangian with the ordinary SL(2,C), but retains a structure similar to N=4 SYM, and discusses its potential as an exact symmetry.

Findings

Dual SL(2,C) symmetry does not generate a Yangian.

The algebraic structure resembles that of N=4 SYM.

Possible recovery of dual SL(2,C) symmetry through deformation.

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.