BPS strings and the stability of the asymptotic Casimir law in adjoint flavor-symmetric YMH models

BPS Z(N) String Tensions, Sine Law and Casimir Scaling and Integrable Field Theories

We consider a Yang-Mills-Higgs theory with spontaneous symmetry breaking of the gauge group G -> U(1)^r -> C(G), with C(G) being the center of G. We study two vacua solutions of the theory which produce this symmetry breaking. We show that for one of these vacua, the theory in the Coulomb phase has the mass spectrum of particles and monopoles which is exactly the same as the mass spectrum of particles and solitons of two dimensional affine Toda field theory. That result holds also for N=4 Super Yang-Mills theories. On the other hand, in the Higgs phase, we show that for each of the two vacua t…

1/2-BPS态的广义支配序

A generalized dominance ordering for 1/2-BPS states

本文提出杨图支配序的推广，用于在已知有限数量Casimir算子时区分1/2-BPS态，并给出区分所需算子数上界的猜想及数值与解析证据。

Color superconductivity, BPS strings and monopole confinement in N=2 and N=4 super Yang-Mills theories

We review some recent developments on BPS string solutions and monopole confinement in the Higgs or (color) superconducting phase of deformed N=2 and N=4 super Yang-Mills theories. In particular, the monopole magnetic fluxes are shown to be always integer linear combinations of string fluxes. Moreover, a bound for the threshold length of the string breaking is obtained. When the gauge group SU(N) is broken to Z_N, the BPS string tension satisfies the Casimir scaling law. Furthermore in the SU(3) case the string solutions are such that they allow the formation of a confining system with three m…

BPS states, conserved charges and centres of symmetric group algebras

In $\mathcal{N}=4$ SYM with $U(N)$ gauge symmetry, the multiplicity of half-BPS states with fixed dimension can be labelled by Young diagrams and can be distinguished using conserved charges corresponding to Casimirs of $U(N)$. The information theoretic study of LLM geometries and superstars in the dual $AdS_5 \times S^5$ background has raised a number of questions about the distinguishability of Young diagrams when a finite set of Casimirs are known. Using Schur-Weyl duality relations between unitary groups and symmetric groups, these questions translate into structural questions about the ce…

Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories

We study the electric flux tubes that undertake color confinement in N=2 supersymmetric Yang-Mills theories softly broken down to N=1 by perturbing with the first two Casimir operators. The relevant Abelian Higgs model is not the standard one due to the presence of an off-diagonal coupling among different magnetic U(1) factors. We perform a preliminary study of this model at a qualitative level. BPS vortices are explicitely obtained for particular values of the soft breaking parameters. Generically however, even in the ultrastrong scaling limit, vortices are not critical but live in a "hybrid"…

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

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 cente…