289 research outputs found
From the octagon to the SFT vertex - gluing and multiple wrapping
We compare various ways of decomposing and decompactifying the string field
theory vertex and analyze the relations between them. We formulate axioms for
the octagon and show how it can be glued to reproduce the decompactified
pp-wave SFT vertex which in turn can be glued to recover the exact finite
volume pp-wave Neumann coefficients. The gluing is performed by resumming
multiple wrapping corrections. We observe important nontrivial contributions at
the multiple wrapping level which are crucial for obtaining the exact results.Comment: 25 pages, many small figure
The kinematical AdS5xS5 Neumann coefficient
For the case of two particles a solution of the string field theory vertex
axioms can be factorized into a standard form factor and a kinematical piece
which includes the dependence on the size of the third string. In this paper we
construct an exact solution of the kinematical axioms for AdS5xS5 which
includes all order wrapping corrections w.r.t. the size of the third string.
This solution is expressed in terms of elliptic Gamma functions and ordinary
elliptic functions. The solution is valid at any coupling and we analyze its
weak coupling, pp-wave and large L limit.Comment: 24 pages, 4 figure
String field theory vertex from integrability
We propose a framework for computing the (light cone) string field theory
vertex in the case when the string worldsheet QFT is a generic integrable
theory. The prime example and ultimate goal would be the
superstring theory cubic string vertex and the chief application will be to use
this framework as a formulation for SYM theory OPE coefficients
valid at any coupling up to wrapping corrections. In this paper we propose
integrability axioms for the vertex, illustrate them on the example of the
pp-wave string field theory and also uncover similar structures in weak
coupling computations of OPE coefficients.Comment: pdflatex, 52 pages, 20 figures,v2: references added, typos correcte
HHL correlators, orbit averaging and form factors
We argue that the conventional method to calculate the OPE coefficients in
the strong coupling limit for heavy-heavy-light operators in the N=4
Super-Yang-Mills theory has to be modified by integrating the light vertex
operator not only over a single string worldsheet but also over the moduli
space of classical solutions corresponding to the heavy states. This reflects
the fact that we are primarily interested in energy eigenstates and not
coherent states. We tested our prescription for the BMN vacuum correlator, for
folded strings on and for two-particle states. Our prescription for
two-particle states with the dilaton leads to a volume dependence which matches
exactly to the structure of finite volume diagonal formfactors. As the volume
depence does not rely on the particular light operator we conjecture that
symmetric OPE coefficients can be described for any coupling by finite volume
diagonal form factors.Comment: 32 pages, 1 figure; v2: small corrections including signs, references
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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
Geometry of W-algebras from the affine Lie algebra point of view
To classify the classical field theories with W-symmetry one has to classify
the symplectic leaves of the corresponding W-algebra, which are the
intersection of the defining constraint and the coadjoint orbit of the affine
Lie algebra if the W-algebra in question is obtained by reducing a WZNW model.
The fields that survive the reduction will obey non-linear Poisson bracket (or
commutator) relations in general. For example the Toda models are well-known
theories which possess such a non-linear W-symmetry and many features of these
models can only be understood if one investigates the reduction procedure. In
this paper we analyze the SL(n,R) case from which the so-called W_n-algebras
can be obtained. One advantage of the reduction viewpoint is that it gives a
constructive way to classify the symplectic leaves of the W-algebra which we
had done in the n=2 case which will correspond to the coadjoint orbits of the
Virasoro algebra and for n=3 which case gives rise to the Zamolodchikov
algebra. Our method in principle is capable of constructing explicit
representatives on each leaf. Another attractive feature of this approach is
the fact that the global nature of the W-transformations can be explicitly
described. The reduction method also enables one to determine the ``classical
highest weight (h. w.) states'' which are the stable minima of the energy on a
W-leaf. These are important as only to those leaves can a highest weight
representation space of the W-algebra be associated which contains a
``classical h. w. state''.Comment: 17 pages, LaTeX, revised 1. and 7. chapter
From Defects to Boundaries
In this paper we describe how relativistic field theories containing defects
are equivalent to a class of boundary field theories. As a consequence
previously derived results for boundaries can be directly applied to defects,
these results include reduction formulas, the Coleman-Thun mechanism and
Cutcosky rules. For integrable theories the defect crossing unitarity equation
can be derived and defect operator found. For a generic purely transmitting
impurity we use the boundary bootstrap method to obtain solutions of the defect
Yang-Baxter equation. The groundstate energy on the strip with defects is also
calculated.Comment: 14 pages, 10 figures. V2 Removed comparison to RT algebras and added
paragraph on the usefulness of transmitting defects in the study of boundary
systems. References added. V3 Extended to include application to defect TB
Finite-Volume Spectra of the Lee-Yang Model
We consider the non-unitary Lee-Yang minimal model in three
different finite geometries: (i) on the interval with integrable boundary
conditions labelled by the Kac labels , (ii) on the circle
with periodic boundary conditions and (iii) on the periodic circle including an
integrable purely transmitting defect. We apply integrable
perturbations on the boundary and on the defect and describe the flow of the
spectrum. Adding a integrable perturbation to move off-criticality
in the bulk, we determine the finite size spectrum of the massive scattering
theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations.
We derive these integral equations for all excitations by solving, in the
continuum scaling limit, the TBA functional equations satisfied by the transfer
matrices of the associated RSOS lattice model of Forrester and Baxter
in Regime III. The excitations are classified in terms of systems. The
excited state TBA equations agree with the previously conjectured equations in
the boundary and periodic cases. In the defect case, new TBA equations confirm
previously conjectured transmission factors.Comment: LateX, 42 pages with 22 eps figure
Five loop Konishi from AdS/CFT
We derive the perturbative five loop anomalous dimension of the
Konishi operator in N = 4 SYM theory from the integrable string
sigma model by evaluating finite size effects using Luscher
formulas adapted to multimagnon states at weak coupling. In
addition, we derive the five loop wrapping contribution for the
L = 2 single impurity state in the beta deformed theory, which
may be within reach of a direct perturbative computation. The
Konishi expression exhibits two new features - a modification of
Asymptotic Bethe Ansatz quantization and sensitiveness to an
infinite set of coefficients of the BES/BHL dressing phase. The
result satisfies nontrivial self-consistency conditions - simple
transcendentality structure and cancellation of mu-term poles.
It may be a testing ground for the proposed AdS/CIFT TBA
systems. (C) 2009 Elsevier B.V. All rights reserved
Exactly solvable model of the 2D electrical double layer
We consider equilibrium statistical mechanics of a simplified model for the
ideal conductor electrode in an interface contact with a classical
semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of
pointlike unit charges in the stability-against-collapse regime of
reduced inverse temperatures . If there is a potential difference
between the bulk interior of the electrolyte and the grounded interface, the
electrolyte region close to the interface (known as the electrical double
layer) carries some nonzero surface charge density. The model is mappable onto
an integrable semi-infinite sine-Gordon theory with Dirichlet boundary
conditions. The exact form-factor and boundary state information gained from
the mapping provide asymptotic forms of the charge and number density profiles
of electrolyte particles at large distances from the interface. The result for
the asymptotic behavior of the induced electric potential, related to the
charge density via the Poisson equation, confirms the validity of the concept
of renormalized charge and the corresponding saturation hypothesis. It is
documented on the non-perturbative result for the asymptotic density profile at
a strictly nonzero that the Debye-H\"uckel limit is a
delicate issue.Comment: 14 page
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