Unifying approaches. Derivation of balitsky hierarchy from the Lipatov effective action

We consider a derivation of the hierarchy of correlators of ordered exponentials directly from the Lipatov's effective action (Lipatov in Nucl Phys B 452:369, 1995; Phys Rep 286:131, 1997; Subnucl Ser 49:131, 2013; Int J Mod Phys Conf Ser 39: 1560082, 2015; Int J Mod Phys A 31(28/29):1645011, 2016; EPJ Web Conf 125: 01010, 2016) formulated in terms of interacting ordered exponentials (Bondarenko and Zubkov in Eur Phys J C 78(8), 617 2018; Bondarenko et al. in Eur Phys J C 81(7):61, 2021). The derivation of the Balitsky equation (Balitsky in Nucl Phys B 463:99, 1996; Phys Rev D 60:014020, 1999; At the frontier of particle physics, vol. 2, p. 1237-1342; Nucl Phys B 629:290, 2002; Phys Rev D 72:074027, 2005) from the hierarchy is discussed as well as the way the sub-leading eikonal corrections to the Balitsky equation arise from the transverse field contribution and sub-leading eikonal corrections to the quark propagator. We outline other possible applications of the proposed calculation scheme.