38 research outputs found
On The Problem of the Quantum Heterotic Vortex
We address the problem of non-Abelian super-QCD, with a Fayet-Iliopoulos
term, as seen from the vortex worldsheet perspective. Together with the FI term
, also a mass for the adjoint superfield enters in the game.
This mass allows the interpolation between and super-QCD. While
the phenomenology of the case () is pretty much understood, much
remains to be clarified for the finite- case. We distinguish, inside the
parameter space spanned by the FI term and the mass , four different
corners where some quantitative statements can be made. These are the regions
where the strong dynamics can, in some approximation, be quantitatively
analyzed. We focus in particular on two questions: 1) Is the quantum vortex BPS
or non-BPS? 2) What is the phase of the internal non-Abelian moduli? We find
that the answer to these questions strongly depends upon the choice of the
linear term in the superpotential. We also try to explain what happens in the
most unexplored, and controversial, region of parameters, that of the quantum
heterotic vortex, where .Comment: 47 pp; v2: typo
The Quantum Dynamics of Heterotic Vortex Strings
We study the quantum dynamics of vortex strings in N=1 SQCD with U(N_c) gauge
group and N_f=N_c quarks. The classical worldsheet of the string has N=(0,2)
supersymmetry, but this is broken by quantum effects. We show how the pattern
of supersymmetry breaking and restoration on the worldsheet captures the
quantum dynamics of the underlying 4d theory. We also find qualitative matching
of the meson spectrum in 4d and the spectrum on the worldsheet.Comment: 13 page
Heterotic Vortex Strings
We determine the low-energy N=(0,2) worldsheet dynamics of vortex strings in
a large class of non-Abelian N=1 supersymmetric gauge theories.Comment: 44 pages, 3 figures. v2: typos corrected, reference adde
Magnetic Catalysis in AdS4
We study the formation of fermion condensates in Anti de Sitter space. In
particular, we describe a novel version of magnetic catalysis that arises for
fermions in asymptotically AdS4 geometries which cap off in the infra-red with
a hard wall. We show that the presence of a magnetic field induces a fermion
condensate in the bulk that spontaneously breaks CP symmetry. From the
perspective of the dual boundary theory, this corresponds to a strongly coupled
version of magnetic catalysis in d=2+1.Comment: 22 pages, 4 figures. v2: References added, factors of 2 corrected,
extra comments added in appendix. v3: extra comments about fermion modes in a
hard wall background. v4: A final factor of
Type I Non-Abelian Superconductors in Supersymmetric Gauge Theories
Non-BPS non-Abelian vortices with CP^1 internal moduli space are studied in
an N=2 supersymmetric U(1) x SU(2) gauge theory with softly breaking adjoint
mass terms. For generic internal orientations the classical force between two
vortices can be attractive or repulsive. On the other hand, the mass of the
scalars in the theory is always less than that of the vector bosons; also, the
force between two vortices with the same CP^1 orientation is always attractive:
for these reasons we interpret our model as a non-Abelian generalization of
type I superconductors. We compute the effective potential in the limit of two
well separated vortices. It is a function of the distance and of the relative
colour-flavour orientation of the two vortices; in this limit we find an
effective description in terms of two interacting CP^1 sigma models. In the
limit of two coincident vortices we find two different solutions with the same
topological winding and, for generic values of the parameters, different
tensions. One of the two solutions is described by a CP^1 effective sigma
model, while the other is just an Abelian vortex without internal degrees of
freedom. For generic values of the parameters, one of the two solutions is
metastable, while there are evidences that the other one is truly stable.Comment: 35 pages, 8 figures. v2: fixed typos and added small comments, v3
removed an unecessary figur
Static Interactions of non-Abelian Vortices
Interactions between non-BPS non-Abelian vortices are studied in non-Abelian
U(1) x SU(N) extensions of the Abelian-Higgs model in four dimensions. The
distinctive feature of a non-Abelian vortex is the presence of an internal
CP^{N-1} space of orientational degrees of freedom. For fine-tuned values of
the couplings, the vortices are BPS and there is no net force between two
static parallel vortices at arbitrary distance. On the other hand, for generic
values of the couplings the interactions between two vortices depend
non-trivially on their relative internal orientations. We discuss the problem
both with a numerical approach (valid for small deviations from the BPS limit)
and in a semi-analytical way (valid at large vortex separations). The
interactions can be classified with respect to their asymptotic property at
large vortex separation. In a simpler fine-tuned model, we find two regimes
which are quite similar to the usual type I/II Abelian superconductors. In the
generic model we find other two new regimes: type I*/II*. Unlike the type I
(type II) case, where the interaction is always attractive (repulsive), the
type I* and II* have both attractive and repulsive interactions depending on
the relative orientation. We have found a rich variety of interactions at small
vortex separations. For some values of the couplings, a bound state of two
static vortices at a non-zero distance exists.Comment: 36 pages, 13 figures; v2 a small comment and a reference adde
Monopoles and Holography
We present a holographic theory in AdS_4 whose zero temperature ground state
develops a crystal structure, spontaneously breaking translational symmetry.
The crystal is induced by a background magnetic field, but requires no chemical
potential. This lattice arises from the existence of 't Hooft-Polyakov monopole
solitons in the bulk which condense to form a classical object known as a
monopole wall. In the infra-red, the magnetic field is screened and there is an
emergent SU(2) global symmetry.Comment: 33 pages, 16 figures; v2: ref adde
Determinant and Weyl anomaly of Dirac operator: a holographic derivation
We present a holographic formula relating functional determinants: the
fermion determinant in the one-loop effective action of bulk spinors in an
asymptotically locally AdS background, and the determinant of the two-point
function of the dual operator at the conformal boundary. The formula originates
from AdS/CFT heuristics that map a quantum contribution in the bulk partition
function to a subleading large-N contribution in the boundary partition
function. We use this holographic picture to address questions in spectral
theory and conformal geometry. As an instance, we compute the type-A Weyl
anomaly and the determinant of the iterated Dirac operator on round spheres,
express the latter in terms of Barnes' multiple gamma function and gain insight
into a conjecture by B\"ar and Schopka.Comment: 11 pages; new comments and references added, typos correcte
Solitons in the Higgs phase -- the moduli matrix approach --
We review our recent work on solitons in the Higgs phase. We use U(N_C) gauge
theory with N_F Higgs scalar fields in the fundamental representation, which
can be extended to possess eight supercharges. We propose the moduli matrix as
a fundamental tool to exhaust all BPS solutions, and to characterize all
possible moduli parameters. Moduli spaces of domain walls (kinks) and vortices,
which are the only elementary solitons in the Higgs phase, are found in terms
of the moduli matrix. Stable monopoles and instantons can exist in the Higgs
phase if they are attached by vortices to form composite solitons. The moduli
spaces of these composite solitons are also worked out in terms of the moduli
matrix. Webs of walls can also be formed with characteristic difference between
Abelian and non-Abelian gauge theories. We characterize the total moduli space
of these elementary as well as composite solitons. Effective Lagrangians are
constructed on walls and vortices in a compact form. We also present several
new results on interactions of various solitons, such as monopoles, vortices,
and walls. Review parts contain our works on domain walls (hep-th/0404198,
hep-th/0405194, hep-th/0412024, hep-th/0503033, hep-th/0505136), vortices
(hep-th/0511088, hep-th/0601181), domain wall webs (hep-th/0506135,
hep-th/0508241, hep-th/0509127), monopole-vortex-wall systems (hep-th/0405129,
hep-th/0501207), instanton-vortex systems (hep-th/0412048), effective
Lagrangian on walls and vortices (hep-th/0602289), classification of BPS
equations (hep-th/0506257), and Skyrmions (hep-th/0508130).Comment: 89 pages, 33 figures, invited review article to Journal of Physics A:
Mathematical and General, v3: typos corrected, references added, the
published versio