181 research outputs found
A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
We probe the long-range spin chain approach to planar N=4 gauge theory at
high loop order. A recently employed hyperbolic spin chain invented by
Inozemtsev is suitable for the SU(2) subsector of the state space up to three
loops, but ceases to exhibit the conjectured thermodynamic scaling properties
at higher orders. We indicate how this may be bypassed while nevertheless
preserving integrability, and suggest the corresponding all-loop asymptotic
Bethe ansatz. We also propose the local part of the all-loop gauge transfer
matrix, leading to conjectures for the asymptotically exact formulae for all
local commuting charges. The ansatz is finally shown to be related to a
standard inhomogeneous spin chain. A comparison of our ansatz to semi-classical
string theory uncovers a detailed, non-perturbative agreement between the
corresponding expressions for the infinite tower of local charge densities.
However, the respective Bethe equations differ slightly, and we end by refining
and elaborating a previously proposed possible explanation for this
disagreement.Comment: 48 pages, 1 figure. v2, further results added: discussion of the
relationship to an inhomogeneous spin chain, normalization in sec 3 unified,
v3: minor mistakes corrected, published versio
Speeding Strings
There is a class of single trace operators in Yang-Mills theory
which are related by the AdS/CFT correspondence to classical string solutions.
Interesting examples of such solutions corresponding to periodic trajectories
of the Neumann system were studied recently. In our paper we study a
generalization of these solutions. We consider strings moving with large
velocities. We show that the worldsheet of the fast moving string can be
considered as a perturbation of the degenerate worldsheet, with the small
parameter being the relativistic factor . The series expansion in
this relativistic factor should correspond to the perturbative expansion in the
dual Yang-Mills theory. The operators minimizing the anomalous dimension in the
sector with given charges correspond to periodic trajectories in the mechanical
system which is closely related to the product of two Neumann systems.Comment: v3: added a reference to the earlier wor
Lessons from : Vacuum structure, Asymptotic Series, Instantons and all that
We discuss two dimensional with fermions in the
fundamental as well as adjoint representation. We find factorial growth in the coefficients of
the large order perturbative expansion. We argue that this behavior is related
to classical solutions of the theory, instantons, thus it has nonperturbative
origin. Phenomenologically such a growth is related to highly excited states in
the spectrum. We also analyze the heavy-light quark system within
operator product expansion (which it turns out to be an asymptotic series).
Some vacuum condensates \la\bar{q}(x_{\mu}D_{\mu})^{2n}q\ra\sim (x^2)^n\cdot
n! which are responsible for this factorial growth are also discussed. We
formulate some general puzzles which are not specific for 2D physics, but are
inevitable features of any asymptotic expansion. We resolve these apparent
puzzles within and we speculate that analogous puzzles might occur in
real 4-dimensional QCD as well.Comment: latex, 26 pages. A final version to appear in Phys. Rev.
The Degasperis-Procesi equation as a non-metric Euler equation
In this paper we present a geometric interpretation of the periodic
Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric
linear connection on the diffeomorphism group of the circle. We also show that
for any evolution in the family of -equations there is neither gain nor loss
of the spatial regularity of solutions. This in turn allows us to view the
Degasperis-Procesi and the Camassa-Holm equation as an ODE on the Fr\'echet
space of all smooth functions on the circle.Comment: 17 page
Classical/quantum integrability in AdS/CFT
We discuss the AdS/CFT duality from the perspective of integrable systems and
establish a direct relationship between the dimension of single trace local
operators composed of two types of scalar fields in N=4 super Yang-Mills and
the energy of their dual semiclassical string states in AdS(5) X S(5). The
anomalous dimensions can be computed using a set of Bethe equations, which for
``long'' operators reduces to a Riemann-Hilbert problem. We develop a unified
approach to the long wavelength Bethe equations, the classical ferromagnet and
the classical string solutions in the SU(2) sector and present a general
solution, governed by complex curves endowed with meromorphic differentials
with integer periods. Using this solution we compute the anomalous dimensions
of these long operators up to two loops and demonstrate that they agree with
string-theory predictions.Comment: 49 pages, 5 figures, LaTeX; v2: complete proof of the two-loop
equivalence between the sigma model and the gauge theory is added. References
added; v4,v5,v6: misprints correcte
Properties of pattern formation and selection processes in nonequilibrium systems with external fluctuations
We extend the phase field crystal method for nonequilibrium patterning to
stochastic systems with external source where transient dynamics is essential.
It was shown that at short time scales the system manifests pattern selection
processes. These processes are studied by means of the structure function
dynamics analysis. Nonequilibrium pattern-forming transitions are analyzed by
means of numerical simulations.Comment: 15 poages, 8 figure
Instanton Corrections to Quark Form Factor at Large Momentum Transfer
Within the Wilson integral formalism, we discuss the structure of
nonperturbative corrections to the quark form factor at large momentum transfer
analyzing the infrared renormalon and instanton effects. We show that the
nonperturbative effects determine the initial value for the perturbative
evolution of the quark form factor and attribute their general structure to the
renormalon ambiguities of the perturbative series. It is demonstrated that the
instanton contributions result in the finite renormalization of the
next-to-leading perturbative result and numerically are characterized by a
small factor reflecting the diluteness of the QCD vacuum within the instanton
liquid model.Comment: Version coincident with the journal publication, 9 pages; REVTe
Local Stability of Dynamical Processes in Random Media
A particular type of random dynamical processes is considered, in which the
stochasticity is introduced through randomly fluctuating parameters. A method
of local multipliers is developed for treating the local stability of such
dynamical processes corresponding to infinite--dimensional dynamical systems.
The method is illustrated by several examples, by the random diffusion
equation, random wave equation, and random Schrodinger equation. The evolution
equation for the density matrix of a quasiopen statistical system subjest to
the action of random surrounding is considered. The stationary solutions to
this equation are found to be unstable against arbitrary small finite random
perturbations. The notion of random structural stability is introduced.Comment: 2 files, 34 pages, late
Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
We analyze in detail the relation between an exactly marginal deformation of
N=4 SYM - the Leigh-Strassler or ``beta-deformation'' - and its string theory
dual (recently constructed in hep-th/0502086) by comparing energies of
semiclassical strings to anomalous dimensions of gauge-theory operators in the
two-scalar sector. We stress the existence of integrable structures on the two
sides of the duality. In particular, we argue that the integrability of strings
in AdS_5 x S^5 implies the integrability of the deformed world sheet theory
with real deformation parameter. We compare the fast string limit of the
worldsheet action in the sector with two angular momenta with the continuum
limit of the coherent state action of an anisotropic XXZ spin chain describing
the one-loop anomalous dimensions of the corresponding operators and find a
remarkable agreement for all values of the deformation parameter. We discuss
some of the properties of the Bethe Ansatz for this spin chain, solve the Bethe
equations for small number of excitations and comment on higher loop properties
of the dilatation operator. With the goal of going beyond the leading order in
the 't Hooft expansion we derive the analog of the Bethe equations on the
string-theory side, and show that they coincide with the thermodynamic limit of
the Bethe equations for the spin chain. We also compute the 1/J corrections to
the anomalous dimensions of operators with large R-charge (corresponding to
strings with angular momentum J) and match them to the 1-loop corrections to
the fast string energies. Our results suggest that the impressive agreement
between the gauge theory and semiclassical strings in AdS_5 x S^5 is part of a
larger picture underlying the gauge/gravity duality.Comment: 50 pages, Latex; v2:typos corrected, references added, clarifications
in sec 8 and Appendix A, a discussion of a rational solution added in section
4.2; v3: minor corrections to coefficients in eq. 2.5, 5.2 and appendix A;
v4: minor misprints correcte
Gluon polarization in the nucleon from quasi-real photoproduction of high-pT hadron pairs
We present a determination of the gluon polarization Delta G/G in the
nucleon, based on the helicity asymmetry of quasi-real photoproduction events,
Q^2<1(GeV/c)^2, with a pair of large transverse-momentum hadrons in the final
state. The data were obtained by the COMPASS experiment at CERN using a 160 GeV
polarized muon beam scattered on a polarized 6-LiD target. The helicity
asymmetry for the selected events is = 0.002 +- 0.019(stat.) +-
0.003(syst.). From this value, we obtain in a leading-order QCD analysis Delta
G/G=0.024 +- 0.089(stat.) +- 0.057(syst.) at x_g = 0.095 and mu^2 =~ 3
(GeV}/c)^2.Comment: 10 pages, 3 figure
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