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156
Temperature quantization from the TBA equations
, 2009
"... We analyze the Thermodynamic Bethe Ansatz equations for the mirror model which determine the ground state energy of the lightcone AdS5 × S5 superstring living on a cylinder. The lightcone momentum of string is equal to the circumference of the cylinder, and is identified with the inverse temperatu ..."
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We analyze the Thermodynamic Bethe Ansatz equations for the mirror model which determine the ground state energy of the lightcone AdS5 × S5 superstring living on a cylinder. The lightcone momentum of string is equal to the circumference of the cylinder, and is identified with the inverse temperature of the mirror model. We show that the natural requirement of the analyticity of the Yfunctions leads to the quantization of the temperature of the mirror model which has never been observed in any other models.
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
LongRange Deformations for Integrable Spin Chains
"... We present a recursion relation for the explicit construction of integrable spin chain Hamiltonians with longrange interactions. Based on arbitrary shortrange (e.g. nearestneighbor) integrable spin chains, it allows to construct an infinite set of conserved longrange charges. We explain the modu ..."
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We present a recursion relation for the explicit construction of integrable spin chain Hamiltonians with longrange interactions. Based on arbitrary shortrange (e.g. nearestneighbor) integrable spin chains, it allows to construct an infinite set of conserved longrange charges. We explain the moduli space of deformation parameters by different classes of generating operators. The rapidity map and dressing phase in the longrange Bethe equations are a result of these deformations. The closed chain asymptotic Bethe equations for longrange spin chains transforming under a generic symmetry algebra are derived. Notably, our construction applies to generalizations of standard nearestneighbor chains such as alternating spin chains. We also discuss relevant properties for its application to planar D = 4, N = 4 and D = 3, N = 6 supersymmetric gauge theories. Finally, we present a map between longrange and inhomogeneous spin chains delivering more insight into
FiniteSize Corrections of the CP 3 Giant Magnons: the Lüscher terms,” [arXiv:0810.0704
 in the SU(2) × SU(2) sector of AdS4 × CP 3 ,” [arXiv:0810.1246
"... We compute classical and first quantum finitesize corrections to the recently found giant magnon solutions in two different subspaces of CP 3. We use the Lüscher approach on the recently proposed exact Smatrix for N = 6 superconformal ChernSimons theory. We compare our results with the string and ..."
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We compute classical and first quantum finitesize corrections to the recently found giant magnon solutions in two different subspaces of CP 3. We use the Lüscher approach on the recently proposed exact Smatrix for N = 6 superconformal ChernSimons theory. We compare our results with the string and algebraic curve computations and find agreement, thus providing a nontrivial test for the new AdS4/CFT3 correspondence within an integrability framework. 1
Finitesize Effects for Single Spike
 JHEP
, 2008
"... We use the reduction of the string dynamics on Rt × S 3 to the NeumannRosochatius integrable system to map all string solutions described by this dynamical system onto solutions of the complex sineGordon integrable model. This mapping relates the parameters in the solutions on both sides of the co ..."
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We use the reduction of the string dynamics on Rt × S 3 to the NeumannRosochatius integrable system to map all string solutions described by this dynamical system onto solutions of the complex sineGordon integrable model. This mapping relates the parameters in the solutions on both sides of the correspondence. In the framework of this approach, we find finitesize string solutions, their images in the (complex) sineGordon system, and the leading finitesize effects of the single spike “E − ∆ϕ ” relation for both Rt × S 2 and Rt × S 3 cases. On leave from Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,
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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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
Threepoint functions in planar N = 4 super YangMills Theory for scalar operators up to length five at the oneloop order
 JHEP
, 2012
"... YangMills Theory for scalar operators up to length five at the oneloop order ..."
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YangMills Theory for scalar operators up to length five at the oneloop order
Finitesize Effect of the Dyonic Giant Magnons in N = 6 super ChernSimons Theory
, 810
"... We consider finitesize effects for the dyonic giant magnon of the type IIA string theory on AdS4 × CP 3 by applying Lüscher µterm formula which is derived from a recently proposed Smatrix for the N = 6 super ChernSimons theory. We compute explicitly the effect for the case of a symmetric configu ..."
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We consider finitesize effects for the dyonic giant magnon of the type IIA string theory on AdS4 × CP 3 by applying Lüscher µterm formula which is derived from a recently proposed Smatrix for the N = 6 super ChernSimons theory. We compute explicitly the effect for the case of a symmetric configuration where the two external bound states, each of A and B particles, have the same momentum p and spin J2. We compare this with the classical string theory result which we computed by reducing it to the NeumannRosochatius system. The two results match perfectly. On leave from Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,
On string integrability  A journey through the twodimensional hidden symmetries in the AdS/CFT dualities
, 2010
"... One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in th ..."
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One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. We review the fundamental concepts and properties of integrability in twodimensional σmodels and in the AdS/CFT context. The first part is focused on the AdS5/CFT4 duality, especially the classical and quantum integrability of the type IIB superstring on AdS5 × S5 are discussed in both pure spinor and GreenSchwarz formulations. The second part is dedicated to the AdS4/CFT3 duality with particular attention to the type IIA superstring on AdS4 × CP 3 and its integrability. This review is based on a shortened and revised version of the author’s PhD thesis, discussed at Uppsala University in September 2009.