Effective action for reggeized gluons, classical gluon field of relativistic color charge and color glass condensate approach

We discuss application of formalism of small-x effective action for reggeized gluons (Gribov, Sov. Phys. JETP 26:414, 1968; Lipatov, Nucl. Phys. B 452:369, 1995; Lipatov, Phys. Rep. 286:131, 1997; Lipatov, Subnucl. Ser. 49:131, 2013; Lipatov, Int. J. Mod. Phys. Conf. Ser. 39:1560082, 2015; Lipatov, Int. J. Mod. Phys. A 31(28/29):1645011, 2016; Lipatov, EPJ Web Conf. 125:01010, 2016; Lipatov, Sov. J. Nucl. Phys. 23:338, 1976; Kuraev et al., Sov. Phys. JETP 45:199, 1977; Kuraev et al., Zh Eksp, Teor. Fiz. 72:377, 1977; Balitsky and Lipatov, Sov. J. Nucl. Phys. 28:822, 1978; Balitsky and Lipatov, Yad. Fiz. 28:1597 1978), for the calculation of classical gluon field of relativistic color charge, similarly to that done in CGC approach of McLerran and Venugopalan, Phys. Rev. D 49:2233 (1994), Jalilian-Marian et al., Phys. Rev. D 55:5414 (1997), Jalilian-Marian et al., Nucl. Phys. B 504:415 (1997), Jalilian-Marian et al., Phys. Rev. D 59:014014 (1998), Jalilian-Marian et al., Phys. Rev. D 59:014015 (1998), Iancu et al., Nucl. Phys. A 692:583 (2001), Iancu et al., Phys. Lett. B 510:133 (2001), Ferreiro et al., Nucl. Phys. A 703:489 (2002). The equations of motion with the reggeon fields are solved in LO and NLO approximations and new solutions are found. The results are compared to the calculations performed in the CGC framework and it is demonstrated that the LO CGC results for the classical field are reproduced in our calculations. Possible applications of the NLO solution in the effective action and CGC frameworks are discussed as well. (orig.)