56 research outputs found

    Yangian description for decays and possible explanation of XX in the decay KL0→π0π0XK^0_L\to \pi^0 \pi^0 X

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    In this letter, hadronic decay channels of light pseudoscalar mesons are realized in Yangian algebra. In the framework of Yangian, we find that these decay channels can be formulated by acting transition operators, composed of the generators of Yangian, on the corresponding pseudoscalar mesons. This new description of decays allows us to present a possible interpretation of the new unknown particle XX in the decay KL0→π0π0XK^0_L\to \pi^0 \pi^0 X: it is an entangled state of π0\pi^0 and η\eta

    Quantum algebra in the mixed light pseudoscalar meson states

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    In this paper, we investigate the entanglement degrees of pseudoscalar meson states via quantum algebra Y(su(3)). By making use of transition effect of generators J of Y(su(3)), we construct various transition operators in terms of J of Y(su(3)), and act them on eta-pion-eta mixing meson state. The entanglement degrees of both the initial state and final state are calculated with the help of entropy theory. The diagrams of entanglement degrees are presented. Our result shows that a state with desired entanglement degree can be achieved by acting proper chosen transition operator on an initial state. This sheds new light on the connect among quantum information, particle physics and Yangian algebra.Comment: 9 pages, 3 figure

    Integrable Matrix Product States from boundary integrability

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    We consider integrable Matrix Product States (MPS) in integrable spin chains and show that they correspond to "operator valued" solutions of the so-called twisted Boundary Yang-Baxter (or reflection) equation. We argue that the integrability condition is equivalent to a new linear intertwiner relation, which we call the "square root relation", because it involves half of the steps of the reflection equation. It is then shown that the square root relation leads to the full Boundary Yang-Baxter equations. We provide explicit solutions in a number of cases characterized by special symmetries. These correspond to the "symmetric pairs" (SU(N),SO(N))(SU(N),SO(N)) and (SO(N),SO(D)⊗SO(N−D))(SO(N),SO(D)\otimes SO(N-D)), where in each pair the first and second elements are the symmetry groups of the spin chain and the integrable state, respectively. These solutions can be considered as explicit representations of the corresponding twisted Yangians, that are new in a number of cases. Examples include certain concrete MPS relevant for the computation of one-point functions in defect AdS/CFT.Comment: 33 pages, v2: minor corrections, references added, v3: minor modifications, v4: minor modification

    Yangian symmetry applied to Quantum chromodynamics

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    We review applications of Yangain symmetry to high-energy QCD phenomenology. Some basic facts about high-energy QCD are recalled, in particular the spinor-helicity form of scattering amplitudes, the scale evolution equations of deep-inelastic scattering structure functions and the high-energy asymptotics of scattering. As the working tool the Yangian symmetric correlators are introduced and constructed in the framework of the Yangian algebra of gℓ(n)g\ell(n) type. We present the application to the tree scattering amplitudes and their iterative relation, to the parton splitting amplitudes and the kernels of the scale evolution equations of structure functions and to the equations describing the high-energy asymptotics of scattering.Comment: 48 pages, 5 figure

    The hexagon in the mirror: the three-point function in the SoV representation

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    We derive an integral expression for the leading-order type I-I-I three-point functions in the su(2)\mathfrak{su}(2) -sector of N=4\mathcal{N}=4 super Yang-Mills theory, for which no determinant formula is known. To this end, we first map the problem to the partition function of the six vertex model with a hexagonal boundary. The advantage of the six-vertex model expression is that it reveals an extra symmetry of the problem, which is the invariance under 90∘^{\circ} rotation. On the spin-chain side, this corresponds to the exchange of the quantum space and the auxiliary space and is reminiscent of the mirror transformation employed in the worldsheet S-matrix approaches. After the rotation, we then apply Sklyanin's separation of variables (SoV) and obtain a multiple-integral expression of the three-point function. The resulting integrand is expressed in terms of the so-called Baxter polynomials, which is closely related to the quantum spectral curve approach. Along the way, we also derive several new results about the SoV, such as the explicit construction of the basis with twisted boundary conditions and the overlap between the orginal SoV state and the SoV states on the subchains.Comment: 37 pages, 10 figure

    Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

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    We introduce a new class of generalized isotropic Lipkin-Meshkov-Glick models with su(m+1)(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1)(m+1) type. We evaluate in closed form the reduced density matrix of a block of LL spins when the whole system is in its ground state, and study the corresponding von Neumann and R\'enyi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as alog⁥La\log L when LL tends to infinity, where the coefficient aa is equal to (m−k)/2(m-k)/2 in the ground state phase with kk vanishing su(m+1)(m+1) magnon densities. In particular, our results show that none of these generalized Lipkin-Meshkov-Glick models are critical, since when L→∞L\to\infty their R\'enyi entropy RqR_q becomes independent of the parameter qq. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m+1)(m+1) Lipkin-Meshkov-Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m−k≄3m-k\ge3. Finally, in the su(3)(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su(3)(3). This is also true in the su(m+1)(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m+1)(m+1)-simplex in Rm\mathbf R^m whose vertices are the weights of the fundamental representation of su(m+1)(m+1).Comment: Typeset with LaTeX, 32 pages, 3 figures. Final version with corrections and additional reference

    Opérateurs de Heun, ansatz de Bethe et représentations de su(3)su(3)

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    Le prĂ©sent mĂ©moire contient deux articles reliĂ©s par le formalisme de l'ansatz de Bethe. Dans le premier article, l'opĂ©rateur de Heun de type Lie est identifiĂ© comme une spĂ©cialisation de la matrice de transfert d'un modĂšle de BCBC-Gaudin Ă  un site dans un champ magnĂ©tique. Ceci permet de le diagonaliser Ă  l'aide de l'ansatz de Bethe algĂ©brique modifiĂ©. La complĂ©tude du spectre est dĂ©montrĂ©e en reliant les racines de Bethe aux zĂ©ros des solutions polynomiales d'une Ă©quation diffĂ©rentielle de Heun inhomogĂšne. Le deuxiĂšme article aborde le sujet des reprĂ©sentations irrĂ©ductibles de l'algĂšbre de Lie su(3)su(3) dans la rĂ©duction su(3)⊃so(3)⊃so(2)su(3) \supset so(3) \supset so(2). Cette maniĂšre de construire les reprĂ©sentations irrĂ©ductibles de su(3)su(3) porte une ambiguĂŻtĂ© qui empĂȘche de distinguer totalement les vecteurs de base, ce qui mĂšne Ă  un problĂšme d'Ă©tiquette manquante. Dans cet esprit, l'algĂšbre des deux opĂ©rateurs fournissant cette Ă©tiquette est examinĂ©e. L'opĂ©rateur de degrĂ© 4 dans les gĂ©nĂ©rateurs de su(3)su(3) est diagonalisĂ© en se servant des techniques de l'ansatz de Bethe analytique.This Master’s thesis contains two articles linked by the formalism of the Bethe ansatz. In the first article, the Lie-type Heun operator is identified as a specialization of the transfer matrix of a one-site BC-Gaudin model in a magnetic field. This allows its diagonalization by means of the modified algebraic Bethe ansatz. The completeness of the spectrum is proven by relating the Bethe roots to the zeros of the polynomial solutions of an inhomogeneous differential Heun equation. The second article deals with the subject of irreducible representations of the Lie algebra su(3) in the reduction su(3) ⊃ so(3) ⊃ so(2). This way of constructing the irreducible representations of su(3) carries an ambiguity in distinguishing the basis vectors, also known as a missing label problem. In this spirit, the algebra of the two operators providing the missing label is examined. The operator of degree 4 in the generators of su(3) is diagonalized using the techniques of the analytical Bethe ansatz

    New Integrable Models from the Gauge/YBE Correspondence

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    We introduce a class of new integrable lattice models labeled by a pair of positive integers N and r. The integrable model is obtained from the Gauge/YBE correspondence, which states the equivalence of the 4d N=1 S^1 \times S^3/Z_r index of a large class of SU(N) quiver gauge theories with the partition function of 2d classical integrable spin models. The integrability of the model (star-star relation) is equivalent with the invariance of the index under the Seiberg duality. Our solution to the Yang-Baxter equation is one of the most general known in the literature, and reproduces a number of known integrable models. Our analysis identifies the Yang-Baxter equation with a particular duality (called the Yang-Baxter duality) between two 4d N=1 supersymmetric quiver gauge theories. This suggests that the integrability goes beyond 4d lens indices and can be extended to the full physical equivalence among the IR fixed points.Comment: 20 pages, 9 figure
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