239 research outputs found
On Classification of QCD defects via holography
We discuss classification of defects of various codimensions within a
holographic model of pure Yang-Mills theories or gauge theories with
fundamental matter. We focus on their role below and above the phase transition
point as well as their weights in the partition function. The general result is
that objects which are stable and heavy in one phase are becoming very light
(tensionless) in the other phase. We argue that the dependence of the
partition function drastically changes at the phase transition point, and
therefore it correlates with stability properties of configurations. Some
possible applications for study the QCD vacuum properties above and below phase
transition are also discussed.Comment: 21 pages, 2 figure
Particle decay in false vacuum
We revisit the problem of decay of a metastable vacuum induced by the
presence of a particle. For the bosons of the `master field' the problem is
solved in any number of dimensions in terms of the spontaneous decay rate of
the false vacuum, while for a fermion we find a closed expression for the decay
rate in (1+1) dimensions. It is shown that in the (1+1) dimensional case an
infrared problem of one-loop correction to the decay rate of a boson is
resolved due to a cancellation between soft modes of the field. We also find
the boson decay rate in the `sine-Gordon staircase' model in the limits of
strong and weak coupling.Comment: 19 pages, 2 figure
More on the Tensor Response of the QCD Vacuum to an External Magnetic Field
In this Letter we discuss a few issues concerning the magnetic susceptibility
of the quark condensate and the Son-Yamamoto (SY) anomaly matching equation. It
is shown that the SY relation in the IR implies a nontrivial interplay between
the kinetic and WZW terms in the chiral Lagrangian. It is also demonstrated
that in a holographic framework an external magnetic field triggers mixing
between scalar and tensor fields. Accounting for this, one may calculate the
magnetic susceptibility of the quark condensate to all orders in the magnetic
field.Comment: 20 pages, 2 figure
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
On Microscopic Origin of Integrability in Seiberg-Witten Theory
We discuss microscopic origin of integrability in Seiberg-Witten theory,
following mostly the results of hep-th/0612019, as well as present their
certain extension and consider several explicit examples. In particular, we
discuss in more detail the theory with the only switched on higher perturbation
in the ultraviolet, where extra explicit formulas are obtained using
bosonization and elliptic uniformization of the spectral curve.Comment: 24 pages, 1 figure, LaTeX, based on the talks at 'Geometry and
Integrability in Mathematical Physics', Moscow, May 2006; 'Quarks-2006',
Repino, May 2006; Twente conference on Lie groups, December 2006 and
'Classical and Quantum Integrable Models', Dubna, January 200
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
Elliptic Ruijsenaars-Schneider model via the Poisson reduction of the Affine Heisenberg Double
It is shown that the elliptic Ruijsenaars-Schneider model can be obtained
from the affine Heisenberg Double by means of the Poisson reduction procedure.
The dynamical -matrix naturally appears in the construction.Comment: latex, 15 pages, a new section is added where we show that the
problem of solving the equations of motion is equivalent to the factorization
proble
Catalyzed decay of false vacuum in four dimensions
The probability of destruction of a metastable vacuum state by the field of a
highly virtual particle with energy is calculated for a (3+1) dimensional
theory in the leading WKB approximation in the thin-wall limit. It is found
that the induced nucleation rate of bubbles, capable of expansion, is
exponentially small at any energy. The negative exponential power in the rate
reaches its maximum at the energy, corresponding to the top of the barrier in
the bubble energy, where it is a finite fraction of the same power in the
probability of the spontaneous decay of the false vacuum, i.e. at .Comment: 9 pages (standard LaTeX)+ 3 figures (one figure in LaTeX, two are
appended in PostScript). TPI-MINN-92/31-
Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory
We discuss different dualities of QHE in the framework of the noncommutative
Chern-Simons theory. First, we consider the Morita or T-duality transformation
on the torus which maps the abelian noncommutative CS description of QHE on the
torus into the nonabelian commutative description on the dual torus. It is
argued that the Ruijsenaars integrable many-body system provides the
description of the QHE with finite amount of electrons on the torus. The new
IIB brane picture for the QHE is suggested and applied to Jain and generalized
hierarchies. This picture naturally links 2d -model and 3d CS
description of the QHE. All duality transformations are identified in the brane
setup and can be related with the mirror symmetry and S duality. We suggest a
brane interpretation of the plateu transition in IQHE in which a critical point
is naturally described by WZW model.Comment: 31 pages, 4 figure
Exponentiation of Multiparticle Amplitudes in Scalar Theories
It is argued that the amplitudes of the production of soft scalar
particles by one or a few energetic ones in theories like has
the exponential form, , in the regime , ,
, where is the typical kinetic energy of outgoing
particles. Existing results support this conjecture. Several new analytical and
numerical results in favor of the exponential behavior of multiparticle
amplitudes are presented.Comment: Revtex 3.0, 45 pages, 11 figures (some requires bezier.sty, two
postscript figures appended after \end{document}), INR-866/9
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