2,204 research outputs found

    Comments on Supersymmetric Vector and Matrix Models

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    Some results in random matrices are generalized to supermatrices, in particular supermatrix integration is reduced to an integration over the eigenvalues and the resulting volume element is shown to be equivalent to a one dimensional Coulomb gas of both positive and negative charges.It is shown that,for polynomial potentials, after removing the instability due to the annihilation of opposite charges, supermatrix models are indistinguishable from ordinary matrix models, in agreement with a recent result by Alvarez-Gaume and Manes. It is pointed out however that this may not be true for more general potentials such as for instance the supersymmetric generalization of the Penner model.Comment: 6 page

    A super-analogue of Kontsevich's theorem on graph homology

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    In this paper we will prove a super-analogue of a well-known result by Kontsevich which states that the homology of a certain complex which is generated by isomorphism classes of oriented graphs can be calculated as the Lie algebra homology of an infinite-dimensional Lie algebra of symplectic vector fields.Comment: 15 page

    Matrix models as solvable glass models

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    We present a family of solvable models of interacting particles in high dimensionalities without quenched disorder. We show that the models have a glassy regime with aging effects. The interaction is controlled by a parameter pp. For p=2p=2 we obtain matrix models and for p>2p>2 `tensor' models. We concentrate on the cases p=2p=2 which we study analytically and numerically.Comment: 10 pages + 2 figures, Univ.Roma I, 1038/94, ROM2F/94/2

    Crustal failure during binary inspiral

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    We present the first fully relativistic calculations of the crustal strain induced in a neutron star by a binary companion at the late stages of inspiral, employing realistic equations of state for the fluid core and the solid crust. We show that while the deep crust is likely to fail only shortly before coalescence, there is a large variation in elastic strain, with the outermost layers failing relatively early on in the inspiral. We discuss the significance of the results for both electromagnetic and gravitational-wave astronomy.Comment: 5 pages, 3 eps figure

    An infinite genus mapping class group and stable cohomology

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    We exhibit a finitely generated group \M whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface \su of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus gg with nn boundary components, for any g≥0g\geq 0 and n>0n>0. We construct a representation of \M into the restricted symplectic group Spres(Hr){\rm Sp_{res}}({\cal H}_r) of the real Hilbert space generated by the homology classes of non-separating circles on \su, which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first universal Chern class in H^2(\M,\Z) is the pull-back of the Pressley-Segal class on the restricted linear group GLres(H){\rm GL_{res}}({\cal H}) via the inclusion Spres(Hr)⊂GLres(H){\rm Sp_{res}}({\cal H}_r)\subset {\rm GL_{res}}({\cal H}).Comment: 14p., 8 figures, to appear in Commun.Math.Phy

    On an Airy matrix model with a logarithmic potential

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    The Kontsevich-Penner model, an Airy matrix model with a logarithmic potential, may be derived from a simple Gaussian two-matrix model through a duality. In this dual version the Fourier transforms of the n-point correlation functions can be computed in closed form. Using Virasoro constraints, we find that in addition to the parameters tnt_n, which appears in the KdV hierarchies, one needs to introduce here half-integer indices tn/2t_{n/2} . The free energy as a function of those parameters may be obtained from these Virasoro constraints. The large N limit follows from the solution to an integral equation. This leads to explicit computations for a number of topological invariants.Comment: 35 page

    Duality and replicas for a unitary matrix model

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    In a generalized Airy matrix model, a power pp replaces the cubic term of the Airy model introduced by Kontsevich. The parameter pp corresponds to Witten's spin index in the theory of intersection numbers of moduli space of curves. A continuation in pp down to p=−2p= -2 yields a well studied unitary matrix model, which exhibits two different phases in the weak and strong coupling regions, with a third order critical point in-between. The application of duality and replica to the pp-th Airy model allows one to recover both the weak and strong phases of the unitary model, and to establish some new results for these expansions. Therefore the unitary model is also indirectly a generating function for intersection numbers.Comment: 18 page, add referece

    Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models

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    We consider the hungry Volterra hierarchy from the view point of the multi boson KP hierarchy. We construct the hungry Volterra equation as the B\"{a}cklund transformations (BT) which are not the ordinary ones. We call them ``fractional '' BT. We also study the relations between the (discrete time) hungry Volterra equation and two matrix models. From this point of view we study the reduction from (discrete time) 2d Toda lattice to the (discrete time) hungry Volterra equation.Comment: 13 pages, LaTe

    Topological closed-string interpretation of Chern-Simons theory

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    The exact free energy of SU(NN) Chern-Simons theory at level kk is expanded in powers of (N+k)−2.(N+k)^{-2}. This expansion keeps rank-level duality manifest, and simplifies as kk becomes large, keeping NN fixed (or vice versa)---this is the weak-coupling (strong-coupling) limit. With the standard normalization, the free energy on the three-sphere in this limit is shown to be the generating function of the Euler characteristics of the moduli spaces of surfaces of genus g,g, providing a string interpretation for the perturbative expansion. A similar expansion is found for the three-torus, with differences that shed light on contributions from different spacetime topologies in string theory.Comment: 6 pages, iassns-hep-93-30 (title change, omitted refs. added, two sign errors corrected, no significant change

    Compassion motivations: Distinguishing submissive compassion from genuine compassion and its association with shame, submissive behavior, depression, anxiety and stress

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    Abstract Recent research has suggested that being compassionate and helpful to others is linked to well-being. However, people can pursue compassionate motives for different reasons, one of which may be to be liked or valued. Evolutionary theory suggests this form of helping may be related to submissive appeasing behavior and therefore could be negatively associated with well-being. To explore this possibility we developed a new scale called the submissive compassion scale and compared it to other established submissive and shame-based scales, along with measures of depression, anxiety and stress in a group of 192 students. As predicted, a submissive form of compassion (being caring in order to be liked) was associated with submissive behavior, shame-based caring, ego-goals and depression, anxiety, and stress. In contrast, compassionate goals and compassion for others were not. As research on compassion develops, new ways of understanding the complex and mixed motivations that can lie behind compassion are required. The desire to be helpful, kind, and compassionate, when it arises from fears of rejection and desires for acceptance, needs to be explored.N/
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