Tree-level scattering amplitudes in = 4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a `dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action of the dual superconformal generators in on-shell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a Yangian. The non-local Yangian generators acting on amplitudes turn out to be cyclically invariant due to special properties of psu(2,2|4). The representation of the Yangian generators takes the same form as in the case of local operators, suggesting that the Yangian symmetry is an intrinsic property of planar = 4 super Yang-Mills, at least at tree level.

https://iopscience.iop.org/article/10.1088/1126-6708/2009/05/046/pdf

Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory

We establish a direct connection between scattering amplitudes in planar four-dimensional theories and a remarkable mathematical structure known as the positive Grassmannian. The central physical idea is to focus on on-shell diagrams as objects of fundamental importance to scattering amplitudes. We show that the all-loop integrand in N=4 SYM is naturally represented in this way. On-shell diagrams in this theory are intimately tied to a variety of mathematical objects, ranging from a new graphical representation of permutations to a beautiful stratification of the Grassmannian G(k,n) which generalizes the notion of a simplex in projective space. All physically important operations involving on-shell diagrams map to canonical operations on permutations; in particular, BCFW deformations correspond to adjacent transpositions. Each cell of the positive Grassmannian is naturally endowed with positive coordinates and an invariant measure which determines the on-shell function associated with the diagram. This understanding allows us to classify and compute all on-shell diagrams, and give a geometric understanding for all the non-trivial relations among them. Yangian invariance of scattering amplitudes is transparently represented by diffeomorphisms of G(k,n) which preserve the positive structure. Scattering amplitudes in (1+1)-dimensional integrable systems and the ABJM theory in (2+1) dimensions can both be understood as special cases of these ideas. On-shell diagrams in theories with less (or no) supersymmetry are associated with exactly the same structures in the Grassmannian, but with a measure deformed by a factor encoding ultraviolet singularities. The Grassmannian representation of on-shell processes also gives a new understanding of the all-loop integrand for scattering amplitudes, presenting all integrands in a novel dLog form which directly reflects the underlying positive structure.

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Scattering Amplitudes and the Positive Grassmannian

Moving from the mirror theory Bethe?Yang equations proposed by Arutyunov and Frolov, we derive the thermodynamic Bethe ansatz equations which should control the spectrum of the planar AdS5/CFT4 correspondence. The associated set of universal functional relations (Y-system) satisfied by the exponentials of the TBA pseudoenergies is deduced, confirming the structure inferred by Gromov, Kazakov and Vieira.

https://iopscience.iop.org/article/10.1088/1751-8113/42/37/375401/pdf

Thermodynamic Bethe ansatz for planar AdS/CFT: a proposal

We review the recent advances towards finding the spectrum of the AdS5 ? S5 superstring. We thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem. In certain cases our exposition is original and cannot be found in the existing literature. The present part I deals with foundations of classical string theory in AdS5 ? S5, light-cone perturbative quantization and the derivation of the exact light-cone world-sheet scattering matrix.

Foundations of the AdS5 × S5 superstring: I

We use the string hypothesis for the mirror theory to derive the Thermodynamic Bethe Ansatz equations for the AdS5 × S5 mirror model. We further demonstrate how these equations can be used to construct the associated Y-system recently discussed in the literature, putting particular emphasis on the assumptions and the range of validity of the corresponding construction.

Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model

Using the thermodynamic Bethe ansatz method we derive an infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT. The Y-system conjectured in Gromov et al. (Integrability for the Full Spectrum of Planar AdS/CFT. arXiv:0901.3753 [hep-th]) for the spectrum of all operators in planar N = 4 SYM theory follows from these equations. In particular, we present the integral TBA type equations for the spectrum of all operators within the sl(2) sector. We prove that all the kernels and free terms entering these TBA equations are real and have nice fusion properties in the relevant mirror kinematics. We find the analog of DHM formula for the dressing kernel in the mirror kinematics.

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Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory: TBA and excited states

It was made the analysis of influence the geometric imperfections to form on the stability of centrally compressed thin - walled rods of open profile with different wall thickness. The software complex of finite element analysis NASTRAN was used to create computer models of rods. Shelves and walls of rods are modeled as a set of quadrangular shell elements with six degrees of freedom in the node. Geometric imperfections are modeled in the form of the first general form of loss the stability of rods with an ideal surface, which are obtained from the linear calculation of stability which is rigidly fixed at the bottom and articulated at the top. With the help of a specially created program, the amplitude of imperfections in the shape of the rods was proportional to the wall thickness. Calculations of the stability of open-profile rods were performed in a linear formulation by the Lanzosch method, and in a nonlinear formulation by the Newton-Rafson method. Was received the values of the critical load and the corresponding forms of deformation of the rods with an ideal surface and taking into account the imperfections of the shape of different amplitude. The research results of stability of open-profile rods compared to experimental, obtained in 2016 in the laboratory of the Faculty of Civil Engineering, University in Zagreb (Croatia), and analytical and numerical calculations obtained using the ABAQUS software in 2020 at the Faculty of Civil Engineering, Brest State Technical University Faculty (Belarus). Comparative analysis showed that the critical values of compressive forces obtained in this work in the calculations of the stability of the rods in a nonlinear formulation using the computational procedures of the software package NASTRAN, was less than analytical and experimental. The critical forces obtained analytically are bigger than the numerical results of all researchers. The coincidence of numerical values of critical forces was detected in the case of an open profile rod with an ideal surface thickness of 0.0011 m and a mismatch in 0.003 m. The stability of rods research, taking into account the simulated imperfections of the form showed that the increase in the amplitude of imperfections had little effect on the critical values of compressive forces. This indicates that the model of geometric imperfections of the rods in the form of a general form of loss of stability is not the most dangerous for the stability of rods with such a profile, mounting and load. Therefore, there is need in further research of stability of the rods to perform modeling of geometric imperfections, for example, as the forms of their deformation in the ultimate state and from the action of operating load, which are obtained in nonlinear formulation.

Analysis of the loss of stability of open profile thin-walled rods, into account the imperfections of the form

/pdf/effect-of-the-crystallographic-c-axis-orientation-on-the-1ng7qsy7.pdf

Andrii Kozak

Papers

Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory: TBA and excited states

Analysis of the loss of stability of open profile thin-walled rods, into account the imperfections of the form

Effect of the crystallographic c-axis orientation on the tribological properties of the few-layer PtSe2