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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.
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
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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
Toy models for wrapping effects
, 806
"... The anomalous dimensions of local single trace gauge invariant operators in N = 4 supersymmetric YangMills theory can be computed by diagonalizing a long range integrable Hamiltonian by means of a perturbative asymptotic Bethe ansatz. This formalism breaks down when the number of fields of the comp ..."
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The anomalous dimensions of local single trace gauge invariant operators in N = 4 supersymmetric YangMills theory can be computed by diagonalizing a long range integrable Hamiltonian by means of a perturbative asymptotic Bethe ansatz. This formalism breaks down when the number of fields of the composite operator is smaller than the range of the Hamiltonian which coincides with the order in perturbation theory at study. We analyze two spin chain toy models which might shed some light on the physics behind these wrapping effects. One of them, the Hubbard model, is known to be closely related to N = 4 SYM. In this example, we find that the knowledge of the effective spin chain description is insufficient to reconstruct the finite size effects of the underlying electron theory. We compute the wrapping corrections for generic states and relate them to a Luscher like approach. The second toy models are long range integrable Hamiltonians built from the standard algebraic Bethe anstatz formalism. This construction is valid for any symmetry group. In particular, for noncompact groups it exhibits an interesting
Twoloop worldsheet corrections in AdS5 × S 5 superstring
, 704
"... We initiate the computation of the 2loop quantum AdS5 × S 5 string corrections on the example of a certain string configuration in S 5 related by an analytic continuation to a folded rotating string in AdS5 in the “long string ” limit. The 2loop term in the energy of the latter should represent th ..."
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We initiate the computation of the 2loop quantum AdS5 × S 5 string corrections on the example of a certain string configuration in S 5 related by an analytic continuation to a folded rotating string in AdS5 in the “long string ” limit. The 2loop term in the energy of the latter should represent the subleading strongcoupling correction to the cusp anomalous dimension and thus provide a further check of recent conjectures about the exact structure of the Bethe ansatz underlying the AdS/CFT duality. We use the conformal gauge and several choices of the κsymmetry gauge. We present partial results: we compute the bosonic contribution to the effective action and also determine the transcendental form of the fermionic contribution but do not succeed in verifying the cancellation of all logarithmic divergences. The main obstacle appears to be an apparent nonrenormalizability of the GS superstring action which first manifests itself at the 2loop order and leads to subtleties in dealing with power divergent integrals.
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