48,679 research outputs found

    Superconformal index for large N quiver Chern-Simons theories

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    We investigate the N=2 superconformal index for supersymmetric quiver Chern-Simons theories with large N gauge groups. After general arguments about the large N limit, we compute the first few terms in the series expansion of the index for theories proposed as dual theories to homogeneous spaces V^{5,2}, Q^{1,1,1}, Q^{2,2,2}, M^{1,1,1}, and N^{0,1,0}. We confirm that the indices have symmetries expected from the isometries of dual manifolds.Comment: 27 pages, 7 figures; v2: typos corrected, Sec.6 modified; v3: explanation improved, minor corrections, version published in JHE

    Variational Monte Carlo studies of attractive Hubbard model I

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    Normal states of the attractive Hubbard model, especially in two dimension, are studied in the light of a transition from a Fermi liquid to an insulating or gapped state. A series of variational Monte Carlo calculations with better statistics is carried out to estimate accurately expectation values by several many-body wave functions. Although a relatively clear crossover is observed even in the plain Gutzwiller wave function, the states in both regimes are metallic. Meanwhile, a substantial metal-insulator transition takes place at |U|\sim W (band width) in an improved wave function in which intersite correlation is introduced by taking account of virtual states in the second-order perturbation in the infinite-|U| limit. The critical value is favorably compared with recent results of the dynamical-mean-field approximation. In contrast, a conventional Jastrow-type wave functions scarcely improve the normal state. In addition, the issue of Brinkman-Rice metal-insulator transition is reconsidered with much larger systems.Comment: 32 pages (Latex with PTPTeX.sty), with 61 figures. To appear in Prog. Theor. Phys. 108 (2002) vol.

    Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit

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    A class of matrix models which arises as partition function in U(N) Chern-Simons matter theories on three sphere is investigated. Employing the standard technique of the 1/N expansion we solve the system beyond the planar limit. In particular we study a case where the matrix model potential has 1/N correction and give a general solution thereof up to the order of 1/N^2. We confirm that the general solution correctly reproduces the past exact result of the free energy up to the order in the case of pure Chern-Simons theory. We also apply to the matrix model of N=2 Chern-Simons theory with arbitrary numbers of fundamental chiral multiplets and anti-fundamental ones, which does not admit the Fermi gas analysis in general.Comment: 1+29 pages, 2 figures, v2: some improvements, figures added, v3: genus half loop equation solved, calculation for confirmation of the solution, further discussion, improvements, references added, v4: minor improvements, a new example, a reference added, published versio