Interacting branes, dual branes, and dyonic branes: a unifying lagrangian approach in D dimensions

This paper presents a general covariant lagrangian framework for the dynamics of a system of closed n-branes and dual (D-n-4)-branes in D dimensions, interacting with a dynamical (n+1)-form gauge potential. The framework proves sufficiently general to include also a coupling of the branes to (the bosonic sector of) a dynamical supergravity theory. We provide a manifestly Lorentz-invariant and S-duality symmetric Lagrangian, involving the (n+1)-form gauge potential and its dual (D-n-3)-form gauge potential in a symmetric way. The corresponding action depends on generalized Dirac-strings. The requirement of string-independence of the action leads to Dirac-Schwinger quantization conditions for the charges of branes and dual branes, but produces also additional constraints on the possible interactions. It turns out that a system of interacting dyonic branes admits two quantum mechanically inequivalent formulations, involving inequivalent quantization conditions. Asymmetric formulations involving only a single vector potential are also given. For the special cases of dyonic branes in even dimensions known results are easily recovered. As a relevant application of the method we write an effective action which implements the inflow anomaly cancellation mechanism for interacting heterotic strings and five-branes in D=10. A consistent realization of this mechanism requires, in fact, dynamical p-form potentials and a systematic introduction of Dirac-strings.Comment: 36 pages, LaTeX, no figure

Spin-statistics transmutation in relativistic quantum field theories of dyons

We analyse spin and statistics of quantum dyon fields, i.e. fields carrying both electric and magnetic charge, in 3+1 space-time dimensions. It has been shown long time ago that, at the quantum mechanical level, a composite dyon made out of a magnetic pole of charge g and a particle of electric charge e possesses half-integral spin and fermionic statistics, if the constituents are bosons and the Dirac quantization condition $eg=2\pi n$ holds, with n odd. This phenomenon is called spin-statistics transmutation. We show that the same phenomenon occurs at the quantum field theory level for an elementary dyon. This analysis requires the construction of gauge invariant charged dyon fields. Dirac's proposal for such fields, relying on a Coulomb-like photon cloud, leads to quantum correlators exhibiting an unphysical dependence on the Dirac-string. Recently Froehlich and Marchetti proposed a recipe for charged dyon fields, based on a sum over Mandelstam-strings, which overcomes this problem. Using this recipe we derive explicit expressions for the quantum field theory correlators and we provide a proof of the occurrence of spin-statistics transmutation. The proof reduces to a computation of the self-linking numbers of dyon worldlines and Mandelstam strings, projected on a fixed time three-space. Dyon composites are also analysed. The transmutation discussed in this paper bares some analogy with the appearance of anomalous spin and statistics for particles or vortices in Chern-Simons theories in 2+1 dimensions. However, peculiar features appear in 3+1 dimensions e.g. in the spin addition rule.Comment: 32 pages, LaTeX, no figure

The cancellation of worldsheet anomalies in the D=10 Green--Schwarz heterotic string sigma--model

We determine the two--dimensional Weyl, Lorentz and $\kappa$--anomalies in the $D=10$ Green--Schwarz heterotic string sigma--model, in an $SO(1,9)$-Lorentz covariant background gauge, and prove their cancellation.Comment: 12 pages, Plain TeX, no figure

Dirac Branes, Characteristic Currents and Anomaly Cancellations in 5-Branes

The aim of this note is to discuss, in a somewhat informal language, the cancellation of anomalies (in topologically trivial space-time) for 5-branes using as "building blocks": i) a generalization to p-branes of the Dirac strings of monopoles (Dirac branes) and a refinement of this idea involving a geometric regularization of Dirac branes, leading to the formalism of "characteristic currents" ii) the PST formalism . As an example of the potentiality of the developed framework we discuss in some detail the anomaly cancellation in the D=10 effective theory of heterotic string and 5-brane coupled to supergravity, where the anomaly inflow is automatically generated. Some remarks are also made on a similar approach to the problem of anomaly cancellation in the effective theory of M5-brane coupled to D=11 supergravity, developed in collaboration with M.Tonin, where however still as open problem remains a Dirac anomaly.Comment: LaTeX file, espcrc2.sty, 6 pages. Based on the talk given by P.M. at the D.V. Volkov Memorial Conference "Supersymmetry and Quantum Field Theory" (25-29 July, 2000, Kharkov, Ukraine). To be published in Nuclear Physics B Conference Supplement

Evaluation of Teaching and Learning Strategies

With the growing awareness of the importance of teaching and learning in universities and the need to move towards evidence-based teaching, it behooves the professions to re-examine their educational research methodology. While the what, how and why of student learning have become more explicit, the professions still struggle to find valid methods of evaluating the explosion of new innovation in teaching/learning strategies. This paper discusses the problems inherent in applying traditional experimental design techniques to advances in educational practic

Radiation reaction and four-momentum conservation for point-like dyons

We construct for a system of point-like dyons a conserved energy-momentum tensor entailing finite momentum integrals, that takes the radiation reaction into account.Comment: 12 pages, no figure

Chern-kernels and anomaly cancellation in M-theory

This paper deals with magnetic equations of the type dH=J where the current J is a delta-function on a brane worldvolume and H a p-form field strength. In many situations in M-theory this equation needs to be solved for H in terms of a potential. A standard universality class of solutions, involving Dirac-branes, gives rise to strong intermediate singularities in H which in many physically relevant cases lead to inconsistencies. In this paper we present an alternative universality class of solutions for magnetic equations in terms of Chern-kernels, and provide relevant applications, among which the anomaly-free effective action for open M2-branes ending on M5-branes. The unobservability of the Dirac-brane requires a Dirac quantization condition; we show that the requirement of ``unobservability'' of the Chern-kernel leads in M-theory to classical gravitational anomalies which cancel precisely their quantum counterparts.Comment: LaTex, 39 pages, references and comments adde

NS5-branes in IIA supergravity and gravitational anomalies

We construct a gravitational-anomaly-free effective action for the coupled system of IIA D=10 dynamical supergravity interacting with an NS5-brane. The NS5-brane is considered as elementary in that the associated current is a delta-function supported on its worldvolume. Our approach is based on a Chern-kernel which encodes the singularities of the three-form field strength near the brane in an SO(4)-invariant way and provides a solution for its Bianchi identity in terms of a two-form potential. A dimensional reduction of the recently constructed anomaly-free effective action for an elementary M5-brane in D=11 is seen to reproduce our ten-dimensional action. The Chern-kernel approach provides in particular a concrete realization of the anomaly cancellation mechanism envisaged by Witten.Comment: LaTex, 31 pages, no figure

String k-anomalies and D=10 Supergravity constraints: the solution of a puzzle

The $\kappa$--anomaly cancellation mechanism in the heterotic superstring determines the superspace constraints for N=1, D=10 Supergravity--Super--Yang--Mills theory. We point out that the constraints found recently in this way appear to disagree with superspace solutions found in the past. We solve this puzzle establishing perfect agreement between the two methods.Comment: 9 pages, Plain TeX, no figures, Abstract printed as last pag