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2D-4D Correspondence: Towers of Kinks versus Towers of Monopoles in N=2 Theories

We continue to 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 found previously in [1], 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, not all strong-coupling states can be analytically continued to weak coupling to match the observable bound states. At weak coupling, we confirm the existence of bound states of topologically-charged kinks and elementary quanta. Quantization of the U(1) kink modulus leads to formation of towers of such states. For the Z_N-symmetric twisted masses their number is by far less than N-1 as was conjectured previously. We investigate the quasiclassical limit and show that out of N possible towers only two survive in the spectrum for odd N, and a single tower for even N. In the case of CP^2 theory the related CMS are discussed in detail. In these points we overlap and completely agree with the results of Dorey and Petunin. We also comment on 2D-4D correspondence.