Yang-Mills theory for semidirect products G⋉g∗{\rm G}\ltimes\mathfrak{g}^* and its instantons

Yang-Mills theory with a symmetry algebra that is the semidirect product $\mathfrak{h}\ltimes\mathfrak{h}^*$ defined by the coadjoint action of a Lie algebra $\mathfrak{h}$ on its dual $\mathfrak{h}^*$ is studied. The gauge group is the semidirect product ${\rm G}_{\mathfrak{h}}\ltimes{\mathfrak{h}^*}$, a noncompact group given by the coadjoint action on $\mathfrak{h}^*$ of the Lie group ${\rm G}_{\mathfrak{h}}$ of $\mathfrak{h}$. For $\mathfrak{h}$ simple, a method to construct the self-antiself dual instantons of the theory and their gauge non\-equivalent deformations is presented. Every ${\rm G}_{\mathfrak{h}}\ltimes{\mathfrak{h}^*}$ instanton has an embedded ${\rm G}_{\mathfrak{h}}$ instanton with the same instanton charge, in terms of which the construction is realized. As an example,$\mathfrak{h}=\mathfrak{s}\mathfrak{u}(2)$ and instanton charge one is considered. The gauge group is in this case $SU(2)\ltimes{\bf R}^3$. Explicit expressions for the selfdual connection, the zero modes and the metric and complex structures of the moduli space are given.Comment: 21 pages; no figures; typos correcte

Quantization of the open string on plane-wave limits of dS_n x S^n and non-commutativity outside branes

The open string on the plane-wave limit of $dS_n\times S^n$ with constant $B_2$ and dilaton background fields is canonically quantized. This entails solving the classical equations of motion for the string, computing the symplectic form, and defining from its inverse the canonical commutation relations. Canonical quantization is proved to be perfectly suited for this task, since the symplectic form is unambiguously defined and non-singular. The string position and the string momentum operators are shown to satisfy equal-time canonical commutation relations. Noticeably the string position operators define non-commutative spaces for all values of the string world-sheet parameter \sig, thus extending non-commutativity outside the branes on which the string endpoints may be assumed to move. The Minkowski spacetime limit is smooth and reproduces the results in the literature, in particular non-commutativity gets confined to the endpoints.Comment: 31 pages, 12p

BRS symmetry versus supersymmetry in Yang-Mills-Chern-Simons theory

We prove that three-dimensional $N=1$ supersymmetric Yang-Mills-Chern-Simons theory is finite to all loop orders. In general this leaves open the possibility that different regularization methods lead to different finite effective actions. We show that in this model dimensional regularization and regularization by dimensional reduction yield the same effective action. Consequently, the superfield approach preserves BRS invariance for this model.Comment: 27 pages, 2 figures, latex2e, uses epsfi

Higher covariant derivative regulators and non-multiplicative renormalization

The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with dimensional regularization to obtain a consistent renormalized 4-dimensional Yang-Mills theory at the one-loop level. This shows that hybrid regularization methods can be applied not only to finite theories, like \eg\ Chern-Simons, but also to divergent theories.Comment: 12 pages, phyzzx, no figure

Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD

We compute the beta function at one loop for Yang-Mills theory using as regulator the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Faddeev and Slavnov. This regularization prescription has the appealing feature that it is manifestly gauge invariant and essentially four-dimensional. It happens however that the one-loop coefficient in the beta function that it yields is not $-11/3,$ as it should be, but $-23/6.$ The difference is due to unphysical logarithmic radiative corrections generated by the Pauli-Villars determinants on which the regularization method is based. This no-go result discards the prescription as a viable gauge invariant regularization, thus solving a long-standing open question in the literature. We also observe that the prescription can be modified so as to not generate unphysical logarithmic corrections, but at the expense of losing manifest gauge invariance.Comment: 43 pages, Latex file (uses the macro axodraw.sty, instructions of how to get it and use it included), FTUAM 94/9, NIKHEF-H 94/2

Smarandache's function applied to perfect numbers

Smarandache's function may be defined as follows: S(n) = the smallest positive integer such that S(n)! is divisible by n. In this article we are going to see that the value this function takes when n is a perfect number

On the Surface Tensions of Binary Mixtures

For binary mixtures with fixed concentrations of the species, various relationships between the surface tensions and the concentrations are briefly reviewed

Non-integrability of geodesic flow on certain algebraic surfaces

This paper addresses an open problem recently posed by V. Kozlov: a rigorous proof of the non-integrability of the geodesic flow on the cubic surface $x y z=1$. We prove this is the case using the Morales-Ramis theorem and Kovacic algorithm. We also consider some consequences and extensions of this result.Comment: Accepted in Physics Letters