One-dimensional Kac model of dense amorphous hard spheres

We introduce a new model of hard spheres under confinement for the study of the glass and jamming transitions. The model is an one-dimensional chain of the $d$-dimensional boxes each of which contains the same number of hard spheres, and the particles in the boxes of the ends of the chain are quenched at their equilibrium positions. We focus on the infinite dimensional limit ($d \to \infty$) of the model and analytically compute the glass transition densities using the replica liquid theory. From the chain length dependence of the transition densities, we extract the characteristic length scales at the glass transition. The divergence of the lengths are characterized by the two exponents, $-1/4$ for the dynamical transition and $-1$ for the ideal glass transition, which are consistent with those of the $p$-spin mean-field spin glass model. We also show that the model is useful for the study of the growing length scale at the jamming transition.Comment: 6 pages, 4 figure

Three Dimensional Topological Field Theory induced from Generalized Complex Structure

We construct a three-dimensional topological sigma model which is induced from a generalized complex structure on a target generalized complex manifold. This model is constructed from maps from a three-dimensional manifold $X$ to an arbitrary generalized complex manifold $M$. The theory is invariant under the diffeomorphism on the world volume and the $b$-transformation on the generalized complex structure. Moreover the model is manifestly invariant under the mirror symmetry. We derive from this model the Zucchini's two dimensional topological sigma model with a generalized complex structure as a boundary action on $\partial X$. As a special case, we obtain three dimensional realization of a WZ-Poisson manifold.Comment: 18 page

Couplings between a collection of BF models and a set of three-form gauge fields

Consistent interactions that can be added to a free, Abelian gauge theory comprising a collection of BF models and a set of three-form gauge fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of smooth, local, PT invariant, Lorentz covariant, and Poincare invariant interactions, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure modifies the Lagrangian action, the gauge transformations as well as the accompanying algebra.Comment: 17 page

Dressed Quark Propagator at Finite Temperature in the Schwinger-Dyson approach with the Rainbow Approximation - exact numerical solutions and their physical implication

The Schwinger-Dyson equation for the quark in the rainbow approximation at finite temperature (T) is solved numerically without introducing any ansatz for the dressed quark propagator. The dymanical quark mass-function and the wave-function renormalization are found to have non-trivial dependence on three-momentum, Matsubara-frequency and temperature. The critical temperature of the chiral phase transition (T_c) and the T-dependence of the quark condensate are highly affected by the wave-function renormalization. We found that T_c \simeq 155 MeV which is consistent with the result of the finite temperature lattice QCD simulation. It is also found that the system is not a gas of free quarks but a highly interacting system of quarks and gluons even in the chirally symmetric phase.Comment: 13 pages, 8 figures, LaTe

How to Solve Quantum Nonlinear Abelian Gauge Theory in Two Dimension in the Heisenberg Picture

The new method based on the operator formalism proposed by Abe and Nakanishi is applied to the quantum nonlinear abelian gauge theory in two dimension. The soluble models in this method are extended to wider class of quantum field theories. We obtain the exact solution in the canonical-quantization operator formalism in the Heisenberg picture. So this analysis might shed some light on the analysis of gravitational theory and non-polynomial field theories.Comment: LaTeX, 12 pages, to be published in IJMP