T-duality and Differential K-Theory

We give a precise formulation of T-duality for Ramond-Ramond fields. This gives a canonical isomorphism between the "geometrically invariant" subgroups of the twisted differential K-theory of certain principal torus bundles. Our result combines topological T-duality with the Buscher rules found in physics.Comment: 23 pages, typos corrected, submitted to Comm.Math.Phy

Rods are less fragile than spheres: Structural relaxation in dense liquids composed of anisotropic particles

We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in 2D that interact via repulsive contact forces. We measure the structural relaxation times obtained from the long-time decay of the self-part of the intermediate scattering function for the translational and rotational degrees of freedom (DOF) as a function of packing fraction \phi, temperature T, and aspect ratio \alpha. We are able to collapse the \phi and T-dependent structural relaxation times for disks, and dimers and ellipses over a wide range of \alpha, onto a universal scaling function {\cal F}_{\pm}(|\phi-\phi_0|,T,\alpha), which is similar to that employed in previous studies of dense liquids composed of purely repulsive spherical particles in 3D. {\cal F_{\pm}} for both the translational and rotational DOF are characterized by the \alpha-dependent scaling exponents \mu and \delta and packing fraction \phi_0(\alpha) that signals the crossover in the scaling form {\cal F}_{\pm} from hard-particle dynamics to super-Arrhenius behavior for each aspect ratio. We find that the fragility at \phi_0, m(\phi_0), decreases monotonically with increasing aspect ratio for both ellipses and dimers. Moreover, the results for the slow dynamics of dense liquids composed of dimer- and ellipse-shaped particles are qualitatively the same, despite the fact that zero-temperature static packings of dimers are isostatic, while static packings of ellipses are hypostatic.Comment: 10 pages, 17 figures, and 1 tabl

On the Quantum Invariant for the Brieskorn Homology Spheres

We study an exact asymptotic behavior of the Witten-Reshetikhin-Turaev invariant for the Brieskorn homology spheres $\Sigma(p_1,p_2,p_3)$ by use of properties of the modular form following a method proposed by Lawrence and Zagier. Key observation is that the invariant coincides with a limiting value of the Eichler integral of the modular form with weight 3/2. We show that the Casson invariant is related to the number of the Eichler integrals which do not vanish in a limit $\tau\to N \in \mathbb{Z}$. Correspondingly there is a one-to-one correspondence between the non-vanishing Eichler integrals and the irreducible representation of the fundamental group, and the Chern-Simons invariant is given from the Eichler integral in this limit. It is also shown that the Ohtsuki invariant follows from a nearly modular property of the Eichler integral, and we give an explicit form in terms of the L-function.Comment: 26 pages, 2 figure

Association of antihypertensive monotherapy with serum sodium and potassium levels in Chinese patients

<b>Background</b> International guidelines on management of hypertension recommend any major classes of antihypertensive drugs. However, the low prescribing rate of thiazides has been attributed to concerns about electrolyte disturbances and studies between antihypertensive drug classes and hyponatremia/hypokalemia among Chinese patients were scarce. <p></p> <b>Methods</b> From clinical databases we included 2,759 patients who received their first-ever antihypertensive monotherapy from January 2004 to June 2007 in a large territory of Hong Kong. We studied the plasma sodium and potassium levels 8 weeks after prescriptions and factors associated with hyponatremia and hypokalemia by multivariable regression analyses. <p></p> <b>Results</b> Among major antihypertensive drug classes, thiazide users had the lowest sodium level (139.6 mEq/l, 95% confidence interval (CI) 139.3, 140.0, P < 0.001) and patients-prescribed calcium channel blockers (CCBs; 3.92 mEq/l, 95% CI 3.89, 3.95) or thiazide diuretics (3.99 mEq/l, 95% CI 3.93, 4.04) had the lowest potassium levels (P < 0.001). Multivariate analysis reported that advanced age (>/=70 years, odds ratio (OR) 7.49, 95% CI 2.84, 19.8, P < 0.001), male gender (OR 2.38, 95% CI 1.45, 3.91, P < 0.001), and thiazide users (OR 2.42, 95% CI 1.29, 4.56, P = 0.006) were significantly associated with hyponatremia, while renin-angiotensin system (RAS) (OR 0.31, 95% CI 0.13, 0.73, P = 0.008) and beta-blockers (BBs) (OR 0.35, 95% CI 0.23, 0.54, P < 0.001) users were less likely to present with hypokalemia. However, the proportions having normonatremic (95.1%) and normokalemic (89.4%) levels were high. <p></p> <b>Conclusions</b> In view of the low prevalence of hyponatremia and hypokalemia associated with thiazides, physicians should not be deterred from prescribing thiazide diuretics as first-line antihypertensive agents as recommended by most international guidelines

Non-Abelian Chern-Simons models with discrete gauge groups on a lattice

We construct the local Hamiltonian description of the Chern-Simons theory with discrete non-Abelian gauge group on a lattice. We show that the theory is fully determined by the phase factors associated with gauge transformations and classify all possible non-equivalent phase factors. We also construct the gauge invariant electric field operators that move fluxons around and create/anihilate them. We compute the resulting braiding properties of the fluxons. We apply our general results to the simplest class of non-Abelian groups, dihedral groups D_n.Comment: 16 pages, 7 figure

Drinfeld-Manin Instanton and Its Noncommutative Generalization

The Drinfeld-Manin construction of U(N) instanton is reformulated in the ADHM formulism, which gives explicit general solutions of the ADHM constraints for U(N) (N>=2k-1) k-instantons. For the N<2k-1 case, implicit results are given systematically as further constraints, which can be used to the collective coordinate integral. We find that this formulism can be easily generalized to the noncommutative case, where the explicit solutions are as well obtained.Comment: 17 pages, LaTeX, references added, mailing address added, clarifications adde

The boundary field theory induced by the Chern-Simons theory

The Chern-Simons theory defined on a 3-dimensional manifold with boundary is written as a two-dimensional field theory defined only on the boundary of the three-manifold. The resulting theory is, essentially, the pullback to the boundary of a symplectic structure defined on the space of auxiliary fields in terms of which the connection one-form of the Chern-Simons theory is expressed when solving the condition of vanishing curvature. The counting of the physical degrees of freedom living in the boundary associated to the model is performed using Dirac's canonical analysis for the particular case of the gauge group SU(2). The result is that the specific model has one physical local degree of freedom. Moreover, the role of the boundary conditions on the original Chern- Simons theory is displayed and clarified in an example, which shows how the gauge content as well as the structure of the constraints of the induced boundary theory is affected.Comment: 10 page

Self-consistent variational theory for globules

A self-consistent variational theory for globules based on the uniform expansion method is presented. This method, first introduced by Edwards and Singh to estimate the size of a self-avoiding chain, is restricted to a good solvent regime, where two-body repulsion leads to chain swelling. We extend the variational method to a poor solvent regime where the balance between the two-body attractive and the three-body repulsive interactions leads to contraction of the chain to form a globule. By employing the Ginzburg criterion, we recover the correct scaling for the $\theta$-temperature. The introduction of the three-body interaction term in the variational scheme recovers the correct scaling for the two important length scales in the globule - its overall size $R$, and the thermal blob size $\xi_{T}$. Since these two length scales follow very different statistics - Gaussian on length scales $\xi_{T}$, and space filling on length scale $R$ - our approach extends the validity of the uniform expansion method to non-uniform contraction rendering it applicable to polymeric systems with attractive interactions. We present one such application by studying the Rayleigh instability of polyelectrolyte globules in poor solvents. At a critical fraction of charged monomers, $f_c$, along the chain backbone, we observe a clear indication of a first-order transition from a globular state at small $f$, to a stretched state at large $f$; in the intermediate regime the bistable equilibrium between these two states shows the existence of a pearl-necklace structure.Comment: 7 pages, 1 figur