Pis’ma v ZhETF, vol. 105, iss. 1, pp. 53 – 54 2017 January 10 c Non-Abelian vortex in four dimensions as a critical Superstring M. Shifmana, A.Yunga,b,c1) aWilliam I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455, USA bNational Research Center “Kurchatov Institute”, Petersburg Nuclear Physics Institute, Gatchina, 188300 St. Petersburg, Russia cSt. <...> Petersburg State University, 199034 St. Petersburg, Russia Submitted 2 November 2016 DOI: 10.7868/S0370274X17010131 In this paper we review the recent discovery of non-Abelian solitonic vortices [1–4] supported in certain four-dimensional N = 2 supersymmetric Yang– Milles theory with matter which behave as critical tendimensional superstrings. <...> In QCD, the Regge trajectories show almost perfect linear J behavior (J stands for spin). <...> However, in all controllable examples at weak coupling a solitonic confining string exhibits linear behavior for the Regge trajectories only at asymptotically large spins [5, 6]. <...> The reason for this is that at J ∼ 1 the physical “string” becomes short and thick and cannot yield linear Regge behavior. <...> Linear Regge trajectories at J ∼ 1 have a chance to emerge only if the string at hand satisfies the thin-string condition [7], T ≪m2, (1) where T is the string tension and m is a typical mass scale of the bulk fields forming the string. <...> The question weather one can find an example of a solitonic string which might produce linear Regge tra1)e-mail: yung@thd.pnpi.spb.ru Письма вЖЭТФ том 105 вып. 1 – 2 2017 53 jectories at J ∼ 1 was addressed and answered in [7]. <...> In [7] it was shown that (i) and (ii) above are met by the non-Abelian vortex string [1–4] supported in four-dimensional N = 2 supersymmetric QCD with the U(N) gauge group, Nf = 2N matter hypermultiplets and the Fayet-Iliopoulos (FI) parameter ξ [11]. <...> The nonAbelian part of the gauge group has the vanishing β function. (We will need to consider N = 2.) The non-Abelian vortex string is 1/2 BPS saturated <...>