P- and T-violating πNN\pi N N form factor

The form factor of the parity and time-reversal violating (PTV) pion-nucleon interaction is calculated from one-loop vertex diagrams. The degrees of freedom included in the effective lagrangian are nucleons, pions, $\eta$, $\rho$ and $\omega$ mesons. We show that by studying the form factor one can constrain the PTV meson-nucleon coupling constants. We evaluate the mean square radius associated with the PTV $\pi N N$ vertex. Using the mean square radius, we estimate the effect of the PTV $\pi N N$ vertex on the neutron electric dipole moment, and find a very small correction. We also extract the renormalisation group $\beta$ function and use it to discuss evolution of the PTV $\pi N N$ coupling constant beyond the hadronic mass scale.Comment: 14 pages, 2 figures. Added discussion of neutron EDM; to be published in Nucl.Phys.

Sylvester-t' Hooft generators of sl(n) and sl(n|n), and relations between them

Among the simple finite dimensional Lie algebras, only sl(n) possesses two automorphisms of finite order which have no common nonzero eigenvector with eigenvalue one. It turns out that these automorphisms are inner and form a pair of generators that allow one to generate all of sl(n) under bracketing. It seems that Sylvester was the first to mention these generators, but he used them as generators of the associative algebra of all n times n matrices Mat(n). These generators appear in the description of elliptic solutions of the classical Yang-Baxter equation, orthogonal decompositions of Lie algebras, 't Hooft's work on confinement operators in QCD, and various other instances. Here I give an algorithm which both generates sl(n) and explicitly describes a set of defining relations. For simple (up to center) Lie superalgebras, analogs of Sylvester generators exist only for sl(n|n). The relations for this case are also computed.Comment: 14 pages, 6 figure

On Isosystolic Inequalities for T^n, RP^n, and M^3

If a closed smooth n-manifold M admits a finite cover whose Z/2Z-cohomology has the maximal cup-length, then for any riemannian metric g on M, we show that the systole Sys(M,g) and the volume Vol(M,g) of the riemannian manifold (M,g) are related by the following isosystolic inequality: Sys(M,g)^n \leq n! Vol(M,g). The inequality can be regarded as a generalization of Burago and Hebda's inequality for closed essential surfaces and as a refinement of Guth's inequality for closed n-manifolds whose Z/2Z-cohomology has the maximal cup-length. We also establish the same inequality in the context of possibly non-compact manifolds under a similar cohomological condition. The inequality applies to (i) T^n and all other compact euclidean space forms, (ii) RP^n and many other spherical space forms including the Poincar\'e dodecahedral space, and (iii) most closed essential 3-manifolds including all closed aspherical 3-manifolds.Comment: 34 pages, 0 figures. v2 contains expository revisions and some additional reference

Central American Temnocerus Thunberg, 1815 (Coleoptera: Rhynchitidae)

Twenty eight species of Temnocerus Thunberg, 1815 are recognized from Central America (Mexico to Panama) with eight previously described species and 20 new species as follows: T. abdominalis (Voss), T. chiapensis n. sp., T. chiriquensis (Sharp), T. confertus (Sharp), T. cyaneus n. sp., T. ellus n. sp., T. giganteus n. sp., T. guatemalenus (Sharp), T. guerrerensis n. sp., T. herediensis n. sp., T. mexicanus n. sp., T. michoacensis n. sp., T. minutus n. sp., T. niger n. sp., T. oaxacensis n. sp., T. obrieni, n. sp., T. oculatus (Sharp), T. potosi n. sp., T. pseudaeratus n. sp., T. pueblensis n. sp., T. pusillus (Sharp), T. regularis (Sharp), T. rostralis n. sp., T. rugosus n. sp., T. salvensis n. sp., T. tamaulipensis n. sp., T. thesaurus (Sharp) and T. yucatensis n. sp. Rhynchites debilis Sharp is placed in synonymy with Temnocerus guatemalenus (Sharp) and Pselaphorhynchites lindae Hamilton is placed in synonymy with Temnocerus regularis (Sharp). A key to species based on external characters and male genitalia is provided as well as digital images, aedeagus drawings, and map distributions

TTˉT\bar{T} deformations with N=(0,2)\mathcal{N}=(0,2) supersymmetry

We investigate the behaviour of two-dimensional quantum field theories with $\mathcal{N}=(0,2)$ supersymmetry under a deformation induced by the `$T\bar{T}$' composite operator. We show that the deforming operator can be defined by a point-splitting regularisation in such a way as to preserve $\mathcal{N}=(0,2)$ supersymmetry. As an example of this construction, we work out the deformation of a free $\mathcal{N}=(0,2)$ theory and compare to that induced by the Noether stress-energy tensor. Finally, we show that the $\mathcal{N}=(0,2)$ supersymmetric deformed action actually possesses $\mathcal{N}=(2,2)$ symmetry, half of which is non-linearly realised