19 research outputs found
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 monopoles.Comment: 9 pages, 2 figures, invited talk given at 24th Brazilian National
Meeting on Particles and Field
Generalised Abelian Chern-Simons Theories and their Connection to Conformal Field Theories
We discuss the generalization of Abelian Chern-Simons theories when -angles and magnetic monopoles are included. We map sectors of two dimensional
Conformal Field Theories into these three dimensional theories.Comment: 9 page
BPS Z_k strings, string tensions and confinement in non-Abelian Theories
In this talk we review some generalizations of 't Hooft and Mandelstam ideas
on confinement for theories with non-Abelian unbroken gauge groups. In order to
do that, we consider N=2 super Yang-Mills with one flavor and a mass breaking
term. One of the spontaneous symmetry breaking is accomplished by a scalar that
can be in particular in the representation of the diquark condensate and
therefore it can be thought as being itself the condensate. We analyze the
phases of the theory. In the superconducting phase, we show the existence of
BPS Z_k-strings and calculate exactly their string tension in a straightforward
way. We also find that magnetic fluxes of the monopole and Z_k-strings are
proportional to one another allowing for monopole confinement in a phase
transition. We further show that some of the resulting confining theories can
be obtained by adding a deformation term to N=2 or N=4 superconformal theories.Comment: 14 pages, LaTeX (JHEP3), talk given at the Workshop on Integrable
Theories, Solitons and Duality, Sao Paulo, Brazil, 1-6 Jul 2002, (v2) minor
text improvement, (v3) minor text improvemen
Dark Monopoles in Grand Unified Theories
We consider a Yang-Mills-Higgs theory with gauge group broken to
by a Higgs field in the adjoint
representation. We obtain monopole solutions whose magnetic field is not in the
Cartan Subalgebra. Since their magnetic field vanishes in the direction of the
generator of the electromagnetic group , we call them Dark
Monopoles. These Dark Monopoles must exist in some Grand Unified Theories
(GUTs) without the need to introduce a dark sector. We analyze the particular
case of GUT, where we obtain that their mass is , where is a
monotonically increasing function of with
and We also give a
geometrical interpretation to their non-abelian magnetic charge.Comment: 22 pages; added some comments on possible cosmological implications
of Dark Monopoles in the last section and added some references. Published
Versio
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 the ratio of the
tensions of the BPS Z(N) strings satisfy either the Casimir scaling or the sine
law scaling for G=SU(N). These results are extended to other gauge groups: for
the Casimir scaling, the ratios of the tensions are equal to the ratios of the
quadratic Casimir constant of specific representations; for the sine law
scaling, the tensions are proportional to the components of the left
Perron-Frobenius eigenvector of Cartan matrix and the ratios of tensions are
equal to the ratios of the soliton masses of affine Toda field theories.Comment: 21 pages, 10 figures. A correction on the title pag
Solitons and Vertex Operators in Twisted Affine Toda Field Theories
Affine Toda field theories in two dimensions constitute families of
integrable, relativistically invariant field theories in correspondence with
the affine Kac-Moody algebras. The particles which are the quantum excitations
of the fields display interesting patterns in their masses and coupling and
which have recently been shown to extend to the classical soliton solutions
arising when the couplings are imaginary. Here these results are extended from
the untwisted to the twisted algebras. The new soliton solutions and their
masses are found by a folding procedure which can be applied to the affine
Kac-Moody algebras themselves to provide new insights into their structures.
The relevant foldings are related to inner automorphisms of the associated
finite dimensional Lie group which are calculated explicitly and related to
what is known as the twisted Coxeter element. The fact that the twisted affine
Kac-Moody algebras possess vertex operator constructions emerges naturally and
is relevant to the soliton solutions.Comment: 27 pages (harvmac) + 3 figures (LaTex) at the end of the file,
Swansea SWAT/93-94/1