Large-N quantum gauge theories in two dimensions

The partition function of a two-dimensional quantum gauge theory in the large-$N$ limit is expressed as the functional integral over some scalar field. The large-$N$ saddle point equation is presented and solved. The free energy is calculated as the function of the area and of the Euler characteristic. There is no non-trivial saddle point at genus $g>0$. The existence of a non-trivial saddle point is closely related to the weak coupling behavior of the theory. Possible applications of the method to higher dimensions are briefly discussed.Comment: 6pp., Latex, TAUP-2012-92 (revised: few changes, some references added

The Master Field in Generalised QCD2QCD_2

As an illustration of the formalism of the master field we consider generalised $QCD_2$. We show how Wilson Loop averages for an arbitrary contour can be computed explicitly and with some ease. A generalised Hopf equation is shown to govern the behaviour of the eigenvalue density of Wilson loops. The collective field description of the theory is therefore deduced. Finally, the non-trivial master gauge field and field strengths are obtained. These results do not seem easily accessible with conventional means.Comment: 18 pages (big), 2 postscript figures, harvmac, eps

Wilson Loops in Large N QCD on a Sphere

Wilson loop averages of pure gauge QCD at large N on a sphere are calculated by means of Makeenko-Migdal loop equation.Comment: Phys.Lett.B329 (1994) 338 (minor corrections in accordance to published version, several Latex figures are removed and available upon request

El materialismo de Georges Bataille. Una lectura desde Nietzsche y Marx

La noción de materialismo de Georges Bataille se erige como una crítica a las concepciones metafísicas o idealistas del materialismo A partir de una reconstrucción de lo que Bataille expone en distintos lugares de sus escritos de juventud, se propone una interpretación del “bajo materialismo” de Bataille desde su particular lectura de Nietzsche y Marx, que, al intentar hacer compatibles elementos de una y otra filosofía, desemboca en una discusión crítica con ambos autores. Esta discusión que, a su vez, puede ser leída como antecedente de una deconstrucción del materialismo como la que lleva a cabo Jacques Derrida

Exact Solution of the one-impurity quantum Hall problem

The problem of a non-relativistic electron in the presence of a uniform electromagnetic field and of one impurity, described by means of an Aharonov-Bohm point-like vortex, is studied. The exact solution is found and the quantum Hall's conductance turns out to be the same as in the impurity-free case. This exactly solvable model seems to give indications, concerning the possible microscopic mechanisms underlying the integer quantum Hall effect, which sensibly deviate from some proposals available in the literature.Comment: 25 pages, TeX, to appear in J. Phys.

On the large N limit, W_\infty Strings, Star products, AdS/CFT Duality, Nonlinear Sigma Models on AdS spaces and Chern-Simons p-branes

It is shown that the large $N$ limit of SU(N) YM in $curved$ $m$-dim backgrounds can be subsumed by a higher $m+n$ dimensional gravitational theory which can be identified to an $m$-dim generally invariant gauge theory of diffs $N$, where $N$ is an $n$-dim internal space (Cho, Sho, Park, Yoon). Based on these findings, a very plausible geometrical interpretation of the $AdS/CFT$ correspondence could be given. Conformally invariant sigma models in $D=2n$ dimensions with target non-compact SO(2n,1) groups are reviewed. Despite the non-compact nature of the SO(2n,1), the classical action and Hamiltonian are positive definite. Instanton field configurations are found to correspond geometrically to conformal ``stereographic'' mappings of $R^{2n}$ into the Euclidean signature $AdS_{2n}$ spaces. The relation between Self Dual branes and Chern-Simons branes, High Dimensional Knots, follows. A detailed discussion on $W_\infty$ symmetry is given and we outline the Vasiliev procedure to construct an action involving higher spin massless fields in $AdS_4$. This $AdS_4$ spacetime higher spin theory should have a one-to-one correspondence to noncritical $W_\infty$ strings propagating on $AdS_4 \times S^7$.Comment: 43 pages, Tex fil

Calpain Expression in the Brain Cortex after Traumatic Brain Injury

Traumatic brain injury (TBI) is the leading cause of death and disability worldwide. Calpains, a family of cysteine proteases have been implicated in cells death following TBI. Using immunohistochemistry calpain expression was analyzed in post mortem brain tissue obtained from patients who died after TBI, and findings were compared with the brain tissue from patients who died from sudden cardiac arrest. In the injured cortex an increase in calpain expression was observed in all resident brain cells: neurons, glial and endothelial cells in comparison to the control group (all p<0.001). Calpain expression was analyzed in different post-traumatic intervals, from day 0 until 10 days post-injury, in order to establish a time course of expression in the brain cortex after TBI. Expression was detected in the cortex 5 hours after the accident, peaked at 72 hours, and substantially reduced by 10 days after TBI. Calpain expression in the cortex significantly changed during the time from TBI to death (p<0.001), and the most prominent expression was detected in the cortex 3 days after TBI. Our results indicate that prolonged calpain expression in resident brain cells (neurons, glial and endothelial cells) plays an important role in neuronal degeneration following TBI