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Anomalous dimensions of finite size field strength operators
 in N=4 SYM,” arXiv:0710.0217 [hepth
"... ABSTRACT: In the ��super YangMills theory, we consider the higher order anomalous dimensions �of purely gluonic operators Tr�where�is a component of the selfdual field strength. We propose compact closed expressions depending parametrically on that reproduce the prediction of Bethe Ansatz equation ..."
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ABSTRACT: In the ��super YangMills theory, we consider the higher order anomalous dimensions �of purely gluonic operators Tr�where�is a component of the selfdual field strength. We propose compact closed expressions depending parametrically on that reproduce the prediction of Bethe Ansatz equations up to five loop order, including transcendental dressing corrections. The size dependence follows a simple pattern as the perturbative order is increased and suggests hidden relations for these special operators. Contents
On String Smatrix, Bound States and TBA
, 2007
"... The study of finite J effects for the lightcone AdS5 × S5 superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The Smatrices describing t ..."
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Cited by 6 (0 self)
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The study of finite J effects for the lightcone AdS5 × S5 superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The Smatrices describing the scattering of physical excitations in the string and mirror models are related to each other by an analytic continuation. We show that the unitarity requirement for the mirror Smatrix fixes the Smatrices of both theories essentially uniquely. The resulting string Smatrix S(z1, z2) satisfies the generalized unitarity condition and, up to a scalar factor, is a meromorphic function on the elliptic curve associated to each variable z. The double Wick rotation is then accomplished by shifting the variables z by quarter of the imaginary period of the torus. We discuss the apparent bound states of the string and mirror models, and show that depending on a choice of the physical region there are one, two or 2M−1 solutions of the Mparticle bound state equations sharing the same conserved charges. For very large but finite values of J, most of these solutions, however, exhibit various signs of pathological behavior. In particular, they
Analytic Bethe Ansatz Solutions for Highest States in the su(11) and su(2) Sectors
"... We construct the integral equations by taking the thermodynamic limit of both the allloop gauge Bethe ansatz equation and the string Bethe ansatz equation for the highest states in the su(11) and su(2) sectors of the N = 4 super YangMills theory. Using the Fourier transformation we solve the inte ..."
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We construct the integral equations by taking the thermodynamic limit of both the allloop gauge Bethe ansatz equation and the string Bethe ansatz equation for the highest states in the su(11) and su(2) sectors of the N = 4 super YangMills theory. Using the Fourier transformation we solve the integral equations iteratively to obtain the anomalous dimensions of the highest states in the weak coupling expansion. In the su(11) sector we analytically study the strong coupling limit of the anomalous dimension for the allloop gauge Bethe ansatz equation by means of the Laplace transformation.
From nesting to dressing
, 2008
"... In integrable field theories the Smatrix is usually a product of a relatively simple matrix and a complicated scalar factor. We make an observation that in many relativistic integrable field theories the scalar factor can be expressed as a convolution of simple kernels appearing in the nested level ..."
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In integrable field theories the Smatrix is usually a product of a relatively simple matrix and a complicated scalar factor. We make an observation that in many relativistic integrable field theories the scalar factor can be expressed as a convolution of simple kernels appearing in the nested levels of the nested Bethe ansatz. We formulate a proposal, up to some discrete ambiguities, how to reconstruct the scalar factor from the nested Bethe equations and check it for several relativistic integrable field theories. We then apply this proposal to the AdS asymptotic Bethe ansatz and recover the dressing factor in the integral
unknown title
, 712
"... We study a refined large spin limit for twist operators in the sl(2) sector of AdS/CFT. We derive a novel nonperturbative equation for the generalized twoparameter scaling function associated to this limit, and analyze it at weak coupling. It is expected to smoothly interpolate between weakly coup ..."
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We study a refined large spin limit for twist operators in the sl(2) sector of AdS/CFT. We derive a novel nonperturbative equation for the generalized twoparameter scaling function associated to this limit, and analyze it at weak coupling. It is expected to smoothly interpolate between weakly coupled gauge theory and string theory at strong coupling. 1 Introduction, Main Result, and Open Problem The perhaps most interesting subset of all local composite quantum operators of planar N = 4 supersymmetric gauge theory is formed by the sector of sl(2) twist operators. The reason is that these bear many similarities with the twist operators of QCD. They may be symbolically written as
Large spin expansion of the longrange
, 710
"... Preprint typeset in JHEP style HYPER VERSION ..."
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Factorized worldsheet scattering
, 707
"... We show the factorization of the threeparticle worldsheet Smatrix of AdS5×S 5 superstring theory in the nearflatspace limit at one loop order. This is done by computing various scattering amplitudes from Feynman diagrams in the worldsheet theory. The knowledge of certain highest weight amplitu ..."
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We show the factorization of the threeparticle worldsheet Smatrix of AdS5×S 5 superstring theory in the nearflatspace limit at one loop order. This is done by computing various scattering amplitudes from Feynman diagrams in the worldsheet theory. The knowledge of certain highest weight amplitudes allows us to fix all the freedom in the threeparticle Smatrix, which we argue to be constrained up to four scalar functions due to the symmetries of the model. We demonstrate that these amplitudes are given by corresponding products of the known twoparticle Smatrix elements, from which it follows that the scattering of any three worldsheet excitations factorizes. This provides an explicit and direct check of the quantum integrability of string theory in nearflat AdS5 × S 5 as it renders evidence for the existence of higher conserved charges. By computing further amplitudes we also obtain an indirect confirmation of
On String Smatrix, Bound States and TBA
, 2007
"... The study of finite J effects for the lightcone AdS5 × S5 superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The Smatrices describing t ..."
Abstract
 Add to MetaCart
The study of finite J effects for the lightcone AdS5 × S5 superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The Smatrices describing the scattering of physical excitations in the string and mirror models are related to each other by an analytic continuation. We show that the unitarity requirement for the mirror Smatrix fixes the Smatrices of both theories essentially uniquely. The resulting string Smatrix S(z1, z2) satisfies the generalized unitarity condition and, up to a scalar factor, is a meromorphic function on the elliptic curve associated to each variable z. The double Wick rotation is then accomplished by shifting the variables z by quarter of the imaginary period of the torus. We discuss the apparent bound states of the string and mirror models, and show that depending on a choice of the physical region there are one, two or 2M−1 solutions of the Mparticle bound state equations sharing the same conserved charges. For very large but finite values of J, most of these solutions, however, exhibit various signs of pathological behavior. In particular, they