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A one-dimensional quantum particle system in which particles with su(v) spins interact through inverse square interactions is introduced. We refer to it as the SU(v) Calogero spin system. Using the quantum inverse scattering method, we reveal algebraic structures of the system: hidden symmetry is the U(v) − SU(v) U(1) current algebra. This is consistent with the fact that the ground-state wave function is a solution of the Knizhnik-Zamolodchikov equation. Furthermore we show that the system has a higher symmetry, known as the w1 + ∞-algebra. With this W-algebra we have a unified viewpoint on the integrable quantum particle systems with long-range interactions such as the Calogero type (1/x2-interactions) and Sutherland type (1/sin2x-interactions). The Yangian symmetry is briefly discussed. 相似文献
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We use the representation theory of \({\mathcal{N}=2}\) superconformal algebra to study the elliptic genera of Calabi–Yau (CY) D-folds. We compute the entropy of CY manifolds from the growth rate of multiplicities of the massive (non-BPS) representations in the decomposition of their elliptic genera. We find that the entropy of CY manifolds of complex dimension D behaves differently depending on whether D is even or odd. When D is odd, CY entropy coincides with the entropy of the corresponding hyperKähler (D ? 3)-folds due to a structural theorem on Jacobi forms. In particular, we find that the Calabi–Yau 3-fold has a vanishing entropy. At D > 3, using our previous results on hyperKähler manifolds, we find \({S_{CY_D}\sim 2\pi \sqrt{\frac{(D-3)^2}{2(D-1)}n}}\). When D is even, we find the behavior of CY entropy behaving as \({S_{CY_D}\sim 2 \pi\sqrt{\frac{D-1}{2}n}}\). These agree with Cardy’s formula at large D. 相似文献
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S. Hikami 《Physics letters. [Part B]》1981,98(3):208-210
It is shown that the renormalization group ß-functions of the two-dimensional non-linear σ models on various symmetric spaces are determined up to three-loop order by the isomorphic relations between the classical groups. 相似文献
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Commutative elliptic difference operators associated with the affine root systems are constructed in terms of affine R-matrices. These operators describe the Ruijsenaars models with elliptic potentials and reduce to the Macdonald operators in the trigonometric limit. 相似文献
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S. Hikami 《Nuclear Physics B》1983,215(4):555-565
The renormalization group β-function of the non-linear σ model in symmetric spaces is discussed via the isomorphic relation and the reciprocal relation about a parameter α. The four-loop term is investigated and the symmetric properties of the β-function are studied. The four-loop term in the β-function is shown to be vanishing for the orthogonal Anderson localization problem. 相似文献
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The correlation functions of the random variables det(λ−X), in which X is an hermitian N×N random matrix, are known to exhibit universal local statistics in the large N limit. We study here the correlation of those same random variables for real symmetric matrices (GOE). The derivation relies
on an exact dual representation of the problem: the k-point functions are expressed in terms of finite integrals over (quaternionic) k×k matrices. However the control of the Dyson limit, in which the distance of the various parameters λ's is of the order of
the mean spacing, requires an integration over the symplectic group. It is shown that a generalization of the Itzykson–Zuber
method holds for this problem, but contrary to the unitary case, the semi-classical
result requires a finite number of corrections to be exact. We have also considered the problem of an external matrix source coupled to the random
matrix, and obtain explicit integral formulae, which are useful for the analysis of the large N limit.
Received: 19 March 2001 / Accepted: 21 June 2001 相似文献