Title
Non-Abelian string of a finite length
Abstract
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 two-dimensional CP$(N-1)$ model. We analyze both non-supersymmetric (bosonic) model and ${\mathcal N}=(2,2)$ supersymmetric CP$(N-1)$ emerging in the case of 1/2-BPS saturated strings in \ntwo supersymmetric QCD with $N_f=N$.
The non-supersymmetric 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 $L\sim \Lambda_{\rm CP}^{-1}$ (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 L\”usher 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 $L\Lambda_{\rm CP}$. 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 L\”uscher term is absent due to supersymmetry.
Suggested Citation
Monin, Sergey.
(2016).
Non-Abelian string of a finite length.
Retrieved from the University of Minnesota Digital Conservancy,
https://hdl.handle.net/11299/180398.