We consider world-sheet theories for non-Abelian strings assuming compactification on a cylinder with a finite circumference L and periodic boundary conditions. The dynamics of the orientational modes is described by the two-dimensional CP(N-1) model. We analyze both the nonsupersymmetric (bosonic) model and the N=(2,2) supersymmetric CP(N-1) emerging in the case of 1/2-BPS saturated strings (Bogomol'nyi-Prasad-Sommerfteld saturated string that breaks only half of supersymmetry) in N=2 supersymmetric QCD with Nf=N. The nonsupersymmetric case was studied previously; technically our results agree with those obtained previously, although our interpretation is totally different. In the large-N limit we detect a phase transition at L∼ΛCP-1 (which is expected to become a rapid crossover at finite N). If at large L the CP(N-1) model develops a mass gap and is in the Coulomb/confinement phase, with exponentially suppressed finite-L effects, at small L it is in the deconfinement phase, and the orientational modes contribute to the Lüsher term. The latter becomes dependent on the rank of the bulk gauge group. In the supersymmetric CP(N-1) models at finite L we find a large-N solution which was not known previously. We observe a single phase independently of the value of LΛCP. For any value of this parameter a mass gap develops and supersymmetry remains unbroken. So does the SU(N) symmetry of the target space. The mass gap turns out to be independent of the string length. The Lüscher term is absent due to supersymmetry.
|Original language||English (US)|
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|State||Published - Jul 7 2015|