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We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community. [ABSTRACT FROM AUTHOR]

We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications. [ABSTRACT FROM AUTHOR]

Recently, Bern et al. observed that a certain class of next-to-planar Feynman integrals possess a bonus symmetry that is closely related to dual conformal symmetry. It corresponds to a projection of the latter along a certain lightlike direction. Previous studies were performed at the level of the loop integrand, and a Ward identity for the integral was formulated. We investigate the implications of the symmetry at the level of the integrated quantities. In particular, we focus on the phenomenologically important case of five-particle scattering. The symmetry simplifies the four-variable problem to a three-variable one. In the context of the recently proposed space of pentagon functions, the symmetry is much stronger. We find that it drastically reduces the allowed function space, leading to a well-known space of three-variable functions. Furthermore, we show how to use the symmetry in the presence of infrared divergences, where one obtains an anomalous Ward identity. We verify that the Ward identity is satisfied by the leading and subleading poles of several nontrivial five-particle integrals. Finally, we present examples of integrals that possess both ordinary and dual conformal symmetry. [ABSTRACT FROM AUTHOR]

We consider finite-dimensional reductions of an integral operator with the elliptic hypergeometric kernel describing the most general known solution of the Yang-Baxter equation with a rank 1 symmetry algebra. The reduced R-operators reproduce at their bottom the standard Baxter's R-matrix for the 8-vertex model and Sklyanin's L-operator. The general formula has a remarkably compact form and yields new elliptic solutions of the Yang-Baxter equation based on the finite-dimensional representations of the elliptic modular double. The same result is also derived using the fusion formalism. [ABSTRACT FROM AUTHOR]

We study solutions of the Yang-Baxter equation on the tensor product of an arbitrary finite-dimensional and an arbitrary infinite-dimensional representations of rank 1 symmetry algebra. We consider the cases of the Lie algebra sℓ, the modular double (trigonometric deformation), and the Sklyanin algebra (elliptic deformation). The solutions are matrices with operator entries. The matrix elements are differential operators in the case of sℓ, finite-difference operators with trigonometric coefficients in the case of the modular double, or finite-difference operators with coefficients constructed of the Jacobi theta functions in the case of the Sklyanin algebra. We find a new factorized form of the rational, trigonometric, and elliptic solutions, which drastically simplifies them. We show that they are products of several simply organized matrices and obtain for them explicit formulas. Bibliography: 44 titles. [ABSTRACT FROM AUTHOR]

Abstract: Yangian symmetry of amplitudes in super-Yang–Mills theory is formulated in terms of eigenvalue relations for monodromy matrix operators. The Quantum Inverse Scattering Method provides the appropriate tools to treat the extended symmetry and to recover as its consequences many known features like cyclic and inversion symmetry, BCFW recursion, Inverse Soft Limit construction, Grassmannian integral representation, R-invariants and on-shell diagram approach. [Copyright &y& Elsevier]

We construct the R-operator—the solution of the Yang–Baxter equation acting in the tensor product of two infinite-dimensional representations of Faddeev’s modular double. This R-operator intertwines the product of two L-operators associated with the modular double and it is built from three basic operators generating the permutation group of four parameters . [ABSTRACT FROM AUTHOR]

Abstract: Similarity transformations and eigenvalue relations of monodromy operators composed of Jordan–Schwinger type L matrices are considered and used to define Yangian symmetric correlators of n-dimensional theories. Explicit expressions are obtained and relations are formulated. In this way basic notions of the Quantum inverse scattering method provide a convenient formulation for high symmetry and integrability not only in lower dimensions. [Copyright &y& Elsevier]

The R-matrix acting in the tensor product of two spinor representation spaces of Lie algebra so(d) is considered thoroughly. The corresponding Yang-Baxter relation is proved and the underlying localYang-Baxter equation is established. [ABSTRACT FROM AUTHOR]

Abstract: Baxter operators are constructed for quantum spin chains with deformed symmetry. The parallel treatment of Yang–Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier and relying on the factorization regarding parameter permutations is extended to the global chain operators following the scheme worked out recently in the undeformed case. [Copyright &y& Elsevier]

Abstract: We construct Baxter operators for the homogeneous closed XXX spin chain with the quantum space carrying infinite- or finite-dimensional representations. All algebraic relations of Baxter operators and transfer matrices are deduced uniformly from Yang–Baxter relations of the local building blocks of these operators. This results in a systematic and very transparent approach where the cases of finite- and infinite-dimensional representations are treated in analogy. Simple relations between the Baxter operators of both cases are obtained. We represent the quantum spaces by polynomials and build the operators from elementary differentiation and multiplication operators. We present compact explicit formulae for the action of Baxter operators on polynomials. [Copyright &y& Elsevier]

Abstract: This paper presents the second part of our study devoted to the construction of Baxter operators for the homogeneous closed XXX spin chain with the quantum space carrying infinite or finite-dimensional representations. We consider the Baxter operators used in Bazhanov et al. (1996, 1997, 1999, 2010) , formulate their construction uniformly with the construction of our previous paper. The building blocks of all global chain operators are derived from the general Yang–Baxter operators and all operator relations are derived from general Yang–Baxter relations. This leads naturally to the comparison of both constructions and allows to connect closely the treatment of the cases of infinite-dimensional representation of generic spin and finite-dimensional representations of integer or half-integer spin. We prove not only the relations between the operators but present also their explicit forms and expressions for their action on polynomials representing the quantum states. [Copyright &y& Elsevier]

The authors suggest and theoretically study an efficient leaky-wave antenna (LWA) with beam scanning governed by micro-electromechanical systems (MEMS) capacitors. The use of MEMS instead of varactors or magnetised ferrite substrate allows one to significantly decrease losses. The LWA is implemented as a periodically loaded transmission line (PLTL). In order to obtain maximal possible dispersion of a PLTL, resonant loads combining variable capacitors and stub strap inductors are applied. Analysis of dispersion properties and design of a unit cell of the PLTL are based on the analytical model with further numerical optimisation. Full-wave simulations are carried out for a realistic beam-scanning LWA, where the radiated beam can transit from forward to backward directions for a practical MEMS design. [ABSTRACT FROM AUTHOR]

In this paper, we give a self-contained description of three methods of perturbation series summation for the resolvent in the quantum Coulomb problem. Bibliography: 11 titles. [ABSTRACT FROM AUTHOR]

Studies the crystallization of geothite and calcium phosphate in long-chain polymer hydrogel. Use of electronic microscopy to analyze the variation of the number, size and shape of microcrystals formed in the gel; Adherence of the growing microcrystals to polymer chains; Elements influencing the volume of each hybrid structure.

We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms, and rational functions. [ABSTRACT FROM AUTHOR]

We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integrals with constant leading singularities, in D space-time dimensions. These integrals evaluate to Q-linear combinations of multiple polylogarithms of uniform weight at each order in the expansion in the dimensional regularization parameter and are in agreement with previous conjectures for nonplanar pentagon functions. Our results provide the complete set of two-loop Feynman integrals for any massless 2 → 3 scattering process, thereby opening up a new level of precision collider phenomenology. [ABSTRACT FROM AUTHOR]

We compute the symbol of the full-color two-loop five-particle amplitude in N=4 super Yang-Mills theory, including all nonplanar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function. We study the multi-Regge limit of the nonplanar terms, analyze its subleading power corrections, and analytically present the leading logarithmic terms. [ABSTRACT FROM AUTHOR]

We consider finite superamplitudes of N=1 matter, and use superconformal symmetry to derive powerful first-order differential equations for them. Because of on-shell collinear singularities, the Ward identities have an anomaly, which is obtained from lower-loop information. We show that in the five-particle case, the solution to the equations is uniquely fixed by the expected analytic behavior. We apply the method to a nonplanar two-loop five-particle integral. [ABSTRACT FROM AUTHOR]

Possibility of creation of materials with transport properties operated by ultrasound on the basis of thermosensitive hydrogels modified by a solid phase of inorganic compounds is shown. The kinetic model of drug release from the hydrogel matrix, which allows to optimize the parameters of ultrasound exposure is proposed. Various options of devices with operated ultrasound an outlet of medicinal substance are offered. [ABSTRACT FROM AUTHOR]