2,204 research outputs found
Comments on Supersymmetric Vector and Matrix Models
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
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
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
. For we obtain matrix models and for `tensor' models. We
concentrate on the cases which we study analytically and numerically.Comment: 10 pages + 2 figures, Univ.Roma I, 1038/94, ROM2F/94/2
Crustal failure during binary inspiral
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
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 with boundary components, for any and . We
construct a representation of \M into the restricted symplectic group 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
via the inclusion .Comment: 14p., 8 figures, to appear in Commun.Math.Phy
On an Airy matrix model with a logarithmic potential
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 , which appears in the KdV hierarchies,
one needs to introduce here half-integer indices .
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
In a generalized Airy matrix model, a power replaces the cubic term of
the Airy model introduced by Kontsevich. The parameter corresponds to
Witten's spin index in the theory of intersection numbers of moduli space of
curves. A continuation in down to 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 -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
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
The exact free energy of SU() Chern-Simons theory at level is expanded
in powers of This expansion keeps rank-level duality manifest,
and simplifies as becomes large, keeping 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
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
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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