458 research outputs found
Dualities in integrable systems and N=2 theories
We discuss dualities of the integrable dynamics behind the exact solution to
the N=2 SUSY YM theory. It is shown that T duality in the string theory is
related to the separation of variables procedure in dynamical system. We argue
that there are analogues of S duality as well as 3d mirror symmetry in the
many-body systems of Hitchin type governing low-energy effective actions.Comment: 16 pages, Latex, Talk given at QFTHEP-99, Moscow, May 27-June
Spectral Duality in Integrable Systems from AGT Conjecture
We describe relationships between integrable systems with N degrees of
freedom arising from the AGT conjecture. Namely, we prove the equivalence
(spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N)
Gaudin model both at classical and quantum level. The former one appears on the
gauge theory side of the AGT relation in the Nekrasov-Shatashvili (and further
the Seiberg-Witten) limit while the latter one is natural on the CFT side. At
the classical level, the duality transformation relates the Seiberg-Witten
differentials and spectral curves via a bispectral involution. The quantum
duality extends this to the equivalence of the corresponding Baxter-Schrodinger
equations (quantum spectral curves). This equivalence generalizes both the
spectral self-duality between the 2x2 and NxN representations of the Toda chain
and the famous AHH duality
BPS Saturated Vacua Interpolation along One Compact Dimension
A class of generalized Wess-Zumino models with distinct vacua is
investigated. These models allow for BPS saturated vacua interpolation along
one compact spatial dimension. The properties of these interpolations are
studied.Comment: 8 pages, 4 figure
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
Angular Momentum and Gravimagnetization of the SYM vacuum
In this note we discuss the gravimagnetization of the SYM vacuum
in the -background. It is argued that the Seiberg-Witten prepotential
is related to the vacuum density of the angular momentum in the Euclidean
space. The possible role of the dyonic instantons as the microscopic angular
momentum carriers which could yield the spontaneous vacuum gravimagnetization
is conjectured. We interpret the dyonic instanton as a kind of the Euclidean
bounce in similar to one responsible for the Schwinger pair creation. The
induced angular momentum in is also briefly considered in the dual
Liouville formulation of theory via AGT relation.Comment: 20 page
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
Preventing Perinatal Transmission of HIV Costs and Effectiveness of a Recommended Intervention
In the United States, nearly all new human immunodeficiency virus (HIV) infections in children are acquired through perinatal (mother-to-infant) transmission. Each year, approximately 7000 infants are born to HIV-infected women in the United States.1 Without intervention, an estimated 15-30% of these infants would become infected.2 In 1994, results of the AIDS Clinical Trial Group (ACTG) Protocol 076 showed that treatment of infected pregnant women and their infants with zidovudine (ZDV) reduced the rate of perinatal HIV transmission from 25% to 8%.3,4 Following these findings, the Public Health Service (PHS) issued recommendations for ZDV therapy to prevent perinatal HIV transmission5 and for HIV counseling and voluntary testing of pregnant women.
On Integrable Systems and Supersymmetric Gauge Theories
The properties of the N=2 SUSY gauge theories underlying the Seiberg-Witten
hypothesis are discussed. The main ingredients of the formulation of the
finite-gap solutions to integrable equations in terms of complex curves and
generating 1-differential are presented, the invariant sense of these
definitions is illustrated. Recently found exact nonperturbative solutions to
N=2 SUSY gauge theories are formulated using the methods of the theory of
integrable systems and where possible the parallels between standard quantum
field theory results and solutions to integrable systems are discussed.Comment: LaTeX, 38 pages, no figures; based on the lecture given at INTAS
School on Advances in Quantum Field Theory and Statistical Mechanics, Como,
Italy, 1996; minor changes, few references adde
Integrability in QCD and beyond
Yang--Mills theories in four space-time dimensions possess a hidden symmetry
which does not exhibit itself as a symmetry of classical Lagrangians but is
only revealed on the quantum level. It turns out that the effective Yang--Mills
dynamics in several important limits is described by completely integrable
systems that prove to be related to the celebrated Heisenberg spin chain and
its generalizations. In this review we explain the general phenomenon of
complete integrability and its realization in several different situations. As
a prime example, we consider in some detail the scale dependence of composite
(Wilson) operators in QCD and super-Yang--Mills (SYM) theories. High-energy
(Regge) behavior of scattering amplitudes in QCD is also discussed and provides
one with another realization of the same phenomenon that differs, however, from
the first example in essential details. As the third example, we address the
low-energy effective action in a N=2 SYM theory which, contrary to the previous
two cases, corresponds to a classical integrable model. Finally, we include a
short overview of recent attempts to use gauge/string duality in order to
relate integrability of Yang--Mills dynamics with the hidden symmetry of a
string theory on a curved background.Comment: 87 pages, 4 figures; minor stylistic changes, references added. To be
published in the memorial volume 'From Fields to Strings: Circumnavigating
Theoretical Phyiscs', World Scientific, 2004. Dedicated to the memory of Ian
Koga
Comments on Condensates in Non-Supersymmetric Orbifold Field Theories
Non-supersymmetric orbifolds of N=1 super Yang-Mills theories are conjectured
to inherit properties from their supersymmetric parent. We examine this
conjecture by compactifying the Z_2 orbifold theories on a spatial circle of
radius R. We point out that when the orbifold theory lies in the weakly coupled
vacuum of its parent, fractional instantons do give rise to the conjectured
condensate of bi-fundamental fermions. Unfortunately, we show that quantum
effects render this vacuum unstable through the generation of twisted
operators. In the true vacuum state, no fermion condensate forms. Thus, in
contrast to super Yang-Mills, the compactified orbifold theory undergoes a
chiral phase transition as R is varied.Comment: 10 Pages. Added clarifying comments, computational steps and a nice
pretty pictur
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