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2D to 4D Correspondence: Towers of Kinks versus Towers of Monopoles

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models provide for a very attractive playground being a theory imitating some
of the main features of QCD. Those include the asymptotic freedom, mass gap,
confinement, chiral symmetry breaking and others. Furthermore, there is a correspondence between the spectra of
four-dimensional SQCD and N=(2,2) CP(N-1) sigma model which was discovered more
than a decade ago. This correspondence was explained later when it was found
that SQCD supports non-Abelian strings with confined monopoles. The kinks of
the two-dimensional theory are the monopoles attached to the strings. Thus,
analysis of two-dimensional sigma models gives a deeper insight into the four-dimensional SQCD, in particular,
into its strong dynamics.

We study the BPS spectrum of the N=(2,2) CP(N-1) model with the Z_N-symmetric
twisted mass terms. We focus on analysis of the "extra'' towers of states
found previously and compare them to the states that can be identified in the
quasiclassical domain. Exact analysis of the strong-coupling states shows that
not all of them survive when passing to the weak-coupling domain. Some of the states decay on
the curves of the marginal stability (CMS). Thus, most of the strong coupling
states do not exist at weak coupling and cannot be classified quasiclassically.
This result lifts to four dimensions. In terms of the four-dimensional theory,
the "extra" states are the strong coupling dyons, while the
quasiclassical bound states are the bound states of dyons and quarks.