Shift versus no-shift in local regularizations of Chern-Simons theory

We consider a family of local BRS-invariant higher covariant derivative regularizations of $SU(N)$ Chern-Simons theory that do not shift the value of the Chern-Simons parameter $k$ to k+\,{\rm sign}(k)\,\cv at one loop.Comment: phyzzx, 6 pages, FTUAM 94/8, NIKHEF-H 94/14 and UPRF 93/39

Regularization and Renormalization of Chern-Simons Theory

We analyze some features of the perturbative quantization of Chern-Simons theory (CST) in the Landau gauge. In this gauge the theory is known to be perturbatively finite. We consider the renormalization scheme in which the renormalized parameter $k$ equals the bare or classical one and show that it constitutes a natural parametrization for the quantum theory. The reason is that, although in this renormalization scheme the value of the Green functions depends on the regularization used, comparison among different regularization methods shows that the observables (Wilson loops) are the same function of the shifted monodromy parameter $k+c_v$ for all BRS invariant regulators used so far for CST. We also discuss a particular BRS invariant regularization prescription in which CST is perturbatively defined as the large mass limit of dimensionally regularized topologically massive Yang-Mills theory. With this regularization prescription the radiative corrections induced by two-loop contributions do not entail observable consequences since they can be reabsorbed by a finite rescaling of the fields only. This very mechanism is conjectured to take place at higher perturbative orders. Talk presented by G.G. at the NATO AWR on ``Low dimensional Topology and Quantum Field Theory'', 6-13 September 1992, Cambridge (UK).Comment: 10 pages, Phyzzx, LPTHE 92-4

The universality of the shift of the Chern-Simons parameter for a general class of BRS invariant regularizations

We consider a biparametric family of BRS invariant regularization methods of SU(N) Chern-Simons theory (the parameters defining the family taking arbitrary values in \RR^2) and show that the shift $k\to k + sign(k) N$ of the Chern-Simons parameter $k$ occurs for arbitrary values of the family defining parameters. This supports irrefutably the conjecture that the shift of $k$ is universal for BRS invariant regulators.Comment: phyzzx, 7 pages (no figures

Effective Average Action of Chern-Simons Field Theory

The renormalization of the Chern-Simons parameter is investigated by using an exact and manifestly gauge invariant evolution equation for the scale-dependent effective average action.Comment: 14 pages, late

Chern-Simons as a geometrical set up for three dimensional gauge theories

Three dimensional Yang-Mills gauge theories in the presence of the Chern-Simons action are seen as being generated by the pure topological Chern-Simons term through nonlinear covariant redefinitions of the gauge fieldComment: 26 pages, latex2

Physically meaningful and not so meaningful symmetries in Chern-Simons theory

We explicitly show that the Landau gauge supersymmetry of Chern-Simons theory does not have any physical significance. In fact, the difference between an effective action both BRS invariant and Landau supersymmetric and an effective action only BRS invariant is a finite field redefinition. Having established this, we use a BRS invariant regulator that defines CS theory as the large mass limit of topologically massive Yang-Mills theory to discuss the shift k \to k+\cv of the bare Chern-Simons parameter $k$ in conncection with the Landau supersymmetry. Finally, to convince ourselves that the shift above is not an accident of our regularization method, we comment on the fact that all BRS invariant regulators used as yet yield the same value for the shift.Comment: phyzzx, 21 pages, 2 figures in one PS fil

Renormalization Ambiguities in Chern-Simons Theory

We introduce a new family of gauge invariant regularizations of Chern-Simons theories which generate one-loop renormalizations of the coupling constant of the form $k\to k+2 s c_v$ where $s$ can take any arbitrary integer value. In the particular case $s=0$ we get an explicit example of a gauge invariant regularization which does not generate radiative corrections to the bare coupling constant. This ambiguity in the radiative corrections to $k$ is reminiscent of the Coste-L\"uscher results for the parity anomaly in (2+1) fermionic effective actions.Comment: 10 pages, harvmac, no changes, 1 Postscript figure (now included

Centella asiatica l. Phytosome improves cognitive performance by promoting bdnf expression in rat prefrontal cortex

A wide range of people in the world use natural remedies as primary approaches against illnesses. Accordingly, understanding the mechanisms of action of phytochemicals has become of great interest. In this context, Centella asiatica L. is extensively used, not only as anti-inflammatory or antioxidant agent but also as brain tonic. On this basis, the purpose of this study was to evaluate whether the chronic administration of C. asiatica L. to adult male rats was able to improve the expression of Bdnf, one of the main mediators of brain plasticity. Moreover, we assessed whether the treatment could affect the cognitive performance in the novel object recognition (NOR) test. We confirmed the presence of the main compounds in the plasma. Furthermore, C. asiatica L. administration induced an increase of Bdnf in the prefrontal cortex, and the administration of the higher dose of the extract was able to improve cognitive performance. Finally, the increase in the preference index in the NOR test was paralleled by a further increase in Bdnf expression. Overall, we highlight the ability of C. asiatica L. to affect brain functions by increasing Bdnf expression and by enhancing the cognitive performance

Differential Regularization of Topologically Massive Yang-Mills Theory and Chern-Simons Theory

We apply differential renormalization method to the study of three-dimensional topologically massive Yang-Mills and Chern-Simons theories. The method is especially suitable for such theories as it avoids the need for dimensional continuation of three-dimensional antisymmetric tensor and the Feynman rules for three-dimensional theories in coordinate space are relatively simple. The calculus involved is still lengthy but not as difficult as other existing methods of calculation. We compute one-loop propagators and vertices and derive the one-loop local effective action for topologically massive Yang-Mills theory. We then consider Chern-Simons field theory as the large mass limit of topologically massive Yang-Mills theory and show that this leads to the famous shift in the parameter $k$. Some useful formulas for the calculus of differential renormalization of three-dimensional field theories are given in an Appendix.Comment: 25 pages, 4 figures. Several typewritten errors and inappropriate arguments are corrected, especially the correct adresses of authors are give