Edge Singularity in ``Induced QCD"

The behaviour of the master field in ``induced QCD" near the edge of its support is studied. An extended scaling domain, where the shape of the master field is a universal function, is found. This function is determined explicitly for the case of dimensions, close to one, and the $D-1$-expansion is constructed. The problem of the meson spectrum corresponding to this solution is analyzed. As a byproduct of these calculations, a new, explicit equation for the meson spectrum in ``induced QCD" with a general potential is derived.Comment: 23 pages, preprint PUPT-146

“CURING” PYRRHONIAN DOUBT: ANTI-SKEPTICAL RHETORIC IN THE EARLY 18TH CENTURY

By examining the analogies of sickness and disease used by severalopponents of philosophical skepticism (Pyrrhonism) in the early 18th century, this articlewill shed light on the rhetorical strategies used in attempts to undermine the revival ofthis ancient school of philosophy. It will look at the ways in which anti-skeptics discussedthe repercussions of the spread of Pyrrhonism for society and describe how theyproposed to “cure” this so-called disease. A consideration of the strategies will bothreveal some of the assumptions commonly shared by authors of apologetic literature inthe first half of the 18th century and explain why they saw skepticism as such a dangerousphilosophical position

Skepticism and Belief in Early-Modern France: The Fideism of Bishop Pierre Daniel Huet

Despite the seeming oppositions between skepticism and religious belief, Bishop Pierre-Daniel Huet (1630-1721) was both a devout Catholic and a philosophical skeptic. While this opposition may seem paradoxical to both modern readers and Huet’s contemporaries, this thesis explains how Huet’s scandalous posthumous Treatise Concerning the Weakness of Human Understanding (1723) fits into the intellectual curriculum of the seventeenth and early eighteenth centuries. By situating Huet in the intellectual context of Early-Modern France, this thesis demonstrates how philosophical skepticism became appealing to Catholic thinkers both as a polemic and as an epistemological stance in opposition to the rationalist transformation of pre-Enlightenment thought

On the Large N Limit of the Itzykson-Zuber Integral

We study the large N limit of the Itzykson -- Zuber integral and show that the leading term is given by the exponent of an action functional for the complex inviscid Burgers (Hopf) equation evaluated on its particular classical solution; the eigenvalue densities that enter in the IZ integral being the imaginary parts of the boundary values of this solution. We show how this result can be applied to ``induced QCD" with an arbitrary potential $U(x)$. We find that for a nonsingular $U(x)$ in one dimension the eigenvalue density $\rho(x)$ at the saddle point is the solution of the functional equation $G_{+}(G_{-}(x))=G_{-}(G_{+}(x))=x$, where $G_{\pm}(x) \equiv {1\over{2}}U^{\prime}(x)\pm i\pi \rho(x)$. As an illustration we present a number of new particular solutions of the $c=1$ matrix model on a discrete real line.Comment: 19 page

Anomalies and large N limits in matrix string theory

We study the loop expansion for the low energy effective action for matrix string theory. For long string configurations we find the result depends on the ordering of limits. Taking $g_s\to 0$ before $N\to\infty$ we find free strings. Reversing the order of limits however we find anomalous contributions coming from the large $N$ limit that invalidate the loop expansion. We then embed the classical instanton solution into a long string configuration. We find the instanton has a loop expansion weighted by fractional powers of $N$. Finally we identify the scaling regime for which interacting long string configurations have a well defined large $N$ limit. The limit corresponds to large "classical" strings and can be identified with the "dual of the 't Hooft limit, $g_{SYM}^2\sim N$.Comment: 13 pages, 1 figure, harvmac.tex, notational errors corrected, references added. Trivial error in section 5 corrected with the result that the domain of validity of the loop expn. is slightly modifie

Large-N limit of the two-dimensoinal Yang-Mills theory on surfaces with boundaries

The large-N limit of the two-dimensional U$(N)$ Yang-Mills theory on an arbitrary orientable compact surface with boundaries is studied. It is shown that if the holonomies of the gauge field on boundaries are near the identity, then the critical behavior of the system is the same as that of an orientable surface without boundaries with the same genus but with a modified area. The diffenece between this effective area and the real area of the surface is obtained and shown to be a function of the boundary conditions (holonomies) only. A similar result is shown to hold for the group SU$(N)$ and other simple groups.Comment: 11 pages, LaTeX2