Color superconductivity, Z_N flux tubes and monopole confinement in deformed N=2* super Yang-Mills theories

TL;DR

This paper investigates the formation and properties of Z_N flux tubes and monopole confinement in deformed N=2* super Yang-Mills theories, analyzing phases, flux relations, and string tensions.

Contribution

It constructs Z_N flux tube solutions, demonstrates monopole confinement, and verifies Casimir scaling in deformed N=2* super Yang-Mills theories with arbitrary gauge groups.

Findings

Monopoles can be confined by Z_N flux tubes.

String tensions obey Casimir scaling law.

Bound on string-breaking length is established.

Abstract

We study the Z_N flux tubes and monopole confinement in deformed N=2* super Yang-Mills theories. In order to do that we consider an N=4 super Yang-Mills theory with an arbitrary gauge group G and add some N=2, N=1 and N=0 deformation terms. We analyze some possible vacuum solutions and phases of the theory, depending on the deformation terms which are added. In the Coulomb phase for the N=2* theory, G is broken to U(1)^r and the theory has monopole solutions. Then, by adding some deformation terms, the theory passes to the Higgs or color superconducting phase, in which G is broken to its center C_G. In this phase we construct the Z_N flux tubes ansatz and obtain the BPS string tension. We show that the monopole magnetic fluxes are linear integer combinations of the string fluxes and therefore the monopoles can become confined. Then, we obtain a bound for the threshold length of the string-breaking. We also show the possible formation of a confining system with 3 different monopoles for the SU(3) gauge group. Finally we show that the BPS string tensions of the theory satisfy the Casimir scaling law.