307 research outputs found
Multimodal particle size distribution or fractal surface of acrylic acid copolymer nanoparticles: A small-angle X-ray scattering study using direct Fourier and indirect maximum entropy methods
Acrylic acid copolymers are potential carriers for drug delivery. The surface, surface rugosity and the absolute dimension of the particles are parameters that determine the binding of drugs or detergents, diffusion phenomena at the surface and the distribution of the carrier within the human body. The particle-size distribution and surface rugosity of the particles have been investigated by small-angle X-ray scattering and dynamic light scattering. Direct Fourier transform as well as a new strategy for the indirect maximum-entropy method MAXENT are used for data evaluation. Scattering equivalence of a pure multimodal distribution of hard spheres (five populations) and a mixed multimodal-surface-fractal model (four populations) was found. Model calculations and dynamic light-scattering experiments gave evidence of the multimodal particle-size distribution combined with the fractal surface of the carrier The main moiety consists of particles 90 nm in diameter which are surface fractals in the 10 nm region
Twist operators in N=4 beta-deformed theory
In this paper we derive both the leading order finite size corrections for
twist-2 and twist-3 operators and the next-to-leading order finite-size
correction for twist-2 operators in beta-deformed SYM theory. The obtained
results respect the principle of maximum transcendentality as well as
reciprocity. We also find that both wrapping corrections go to zero in the
large spin limit. Moreover, for twist-2 operators we studied the pole structure
and compared it against leading BFKL predictions.Comment: 17 pages; v2: minor changes, references adde
The Bajnok-Janik formula and wrapping corrections
We write down the simplified TBA equations of the string
sigma-model for minimal energy twist-two operators in the sl(2) sector of the
model. By using the linearized version of these TBA equations it is shown that
the wrapping corrected Bethe equations for these states are identical, up to
O(g^8), to the Bethe equations calculated in the generalized L\"uscher approach
(Bajnok-Janik formula). Applications of the Bajnok-Janik formula to
relativistic integrable models, the nonlinear O(n) sigma models for n=2,3,4 and
the SU(n) principal sigma models, are also discussed.Comment: Latex, 22 pages, published versio
Six and seven loop Konishi from Luscher corrections
In the present paper we derive six and seven loop formulas for the anomalous
dimension of the Konishi operator in N=4 SYM from string theory using the
technique of Luscher corrections. We derive analytically the integrand using
the worldsheet S-matrix and evaluate the resulting integral and infinite sum
using a combination of high precision numerical integration and asymptotic
expansion. We use this high precision numerical result to fit the integer
coefficients of zeta values in the final analytical answer. The presented six
and seven loop results can be used as a cross-check with FiNLIE on the string
theory side, or with direct gauge theory computations. The seven loop level is
the theoretical limit of this Luscher approach as at eight loops
double-wrapping corrections will appear.Comment: 18 pages, typos correcte
Konishi operator at intermediate coupling
TBA equations for two-particle states from the sl(2) sector proposed by
Arutyunov, Suzuki and the author are solved numerically for the Konishi
operator descendent up to 't Hooft's coupling lambda ~ 2046. The data obtained
is used to analyze the properties of Y-functions and address the issue of the
existence of the critical values of the coupling. In addition we find a new
integral representation for the BES dressing phase which substantially reduces
the computational time.Comment: lots of figures, v2: improved numerics, c1=2, c2=0, c4 does not
vanis
Lessons from crossing symmetry at large N
20 pages, v2: Assumptions stated more clearly, version published in JHEPWe consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale \Delta_{gap} and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.Peer reviewe
Comments on the Mirror TBA
We discuss various aspects of excited state TBA equations describing the
energy spectrum of the AdS_5 \times S^5 strings and, via the AdS/CFT
correspondence, the spectrum of scaling dimensions of N = 4 SYM local
operators. We observe that auxiliary roots which are used to partially
enumerate solutions of the Bethe-Yang equations do not play any role in
engineering excited state TBA equations via the contour deformation trick. We
further argue that the TBA equations are in fact written not for a particular
string state but for the whole superconformal multiplet, and, therefore, the
psu(2,2|4) invariance is built in into the TBA construction.Comment: 28 pages, 1 figure, v2: misprints are correcte
Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
We consider N=4 SYM and a class of spin N, length-3, twist operators beyond
the well studied sl(2) subsector. They can be identified at one-loop with three
gluon operators. At strong coupling, they are associated with spinning strings
with two spins in AdS5. We exploit the Y-system to compute the leading
weak-coupling four loop wrapping correction to their anomalous dimension. The
result is written in closed form as a function of the spin N. We combine the
wrapping correction with the known four-loop asymptotic Bethe Ansatz
contribution and analyze special limits in the spin N. In particular, at large
N, we prove that a generalized Gribov-Lipatov reciprocity holds. At negative
unphysical spin, we present a simple BFKL-like equation predicting the
rightmost leading poles.Comment: 18 page
Exceptional Operators in N=4 super Yang-Mills
We consider one particularly interesting class of composite gauge-invariant
operators in N=4 super Yang-Mills theory. An exceptional feature of these
operators is that in the Thermodynamic Bethe Ansatz approach the one-loop
rapidities of the constituent magnons are shown to be exact in the 't Hooft
coupling constant. This is used to propose the mirror TBA description for these
operators. The proposal is shown to pass several non-trivial checks.Comment: 40 pages, 2 figures, 1 attached Mathematica noteboo
On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
The centrally extended su(2|2) superalgebra is an asymptotic symmetry of the
light-cone string sigma model on AdS5 x S5. We consider an evaluation
representation of the conventional Yangian built over a particular
16-dimensional long representation of the centrally extended su(2|2).
Interestingly, we find that S-matrices compatible with this evaluation
representation do not exist. On the other hand, by requiring centrally extended
su(2|2) invariance and explicitly solving the Yang-Baxter equation, we find a
scattering matrix for long-short representations of the Lie superalgebra. We
notice that this S-matrix is invariant under a different representation of
non-evaluation type, induced from the tensor product of short representations.
Our findings concern the conventional Yangian only, and are not applied to
possible algebraic extensions of the latter.Comment: Version accepted for publication in JHE
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