Non-perturbative double scaling limits

Recently, the author has proposed a generalization of the matrix and vector models approach to the theory of random surfaces and polymers. The idea is to replace the simple matrix or vector (path) integrals by gauge theory or non-linear sigma model (path) integrals. We explain how this solves one of the most fundamental limitation of the classic approach: we automatically obtain non-perturbative definitions in non-Borel summable cases. This is exemplified on the simplest possible examples involving O(N) symmetric non-linear sigma models with N-dimensional target spaces, for which we construct (multi)critical metrics. The non-perturbative definitions of the double scaled, manifestly positive, partition functions rely on remarkable identities involving (path) integrals.Comment: 18 pages, one figur

Super Yang-Mills, Matrix Models and Geometric Transitions

I explain two applications of the relationship between four dimensional N=1 supersymmetric gauge theories, zero dimensional gauged matrix models, and geometric transitions in string theory. The first is related to the spectrum of BPS domain walls or BPS branes. It is shown that one can smoothly interpolate between a D-brane state, whose weak coupling tension scales as Nc or 1/gs, and a closed string solitonic state, whose weak coupling tension scales as Nc^2 or 1/gs^2. This is part of a larger theory of N=1 quantum parameter spaces. The second is a new purely geometric approach to sum exactly over planar diagrams in zero dimension. It is an example of open/closed string duality.Comment: 11 pages, 2 figures, .cls files included; to appear in the proceedings of the Strings 2004 conference in Pari

Using textual clues to improve metaphor processing

In this paper, we propose a textual clue approach to help metaphor detection, in order to improve the semantic processing of this figure. The previous works in the domain studied the semantic regularities only, overlooking an obvious set of regularities. A corpus-based analysis shows the existence of surface regularities related to metaphors. These clues can be characterized by syntactic structures and lexical markers. We present an object oriented model for representing the textual clues that were found. This representation is designed to help the choice of a semantic processing, in terms of possible non-literal meanings. A prototype implementing this model is currently under development, within an incremental approach allowing step-by-step evaluations. \footnote{This work takes part in a research project sponsored by the AUPELF-UREF (Francophone Agency For Education and Research)}Comment: 3 pages, single LaTeX file, uses aclap.st

Greedy algorithms and poset matroids

We generalize the matroid-theoretic approach to greedy algorithms to the setting of poset matroids, in the sense of Barnabei, Nicoletti and Pezzoli (1998) [BNP]. We illustrate our result by providing a generalization of Kruskal algorithm (which finds a minimum spanning subtree of a weighted graph) to abstract simplicial complexes

Higgs Boson Searches at LEP

The results of the Higgs boson searches performed by the four LEP experiments at centre-of-mass energies between 189 GeV and 209 GeV corresponding to an integrated luminosity of 2461 pb$^{-1}$ are presented here. Searches have been performed for Higgs in the Standard Model (SM), in 2 Higgs Doublet Models (2HDM's), for doubly charged, fermiophobic and invisible Higgs as well as a decay mode independent search. Most of the results of the four experiments have been combined by the LEP Higgs working group.Comment: 8 pages latex, 4 figures include

Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory

We study the physics of N=1 super Yang-Mills theory with gauge group U(Nc) and one adjoint Higgs field, by using the recently derived exact effective superpotentials. Interesting phenomena occur for some special values of the Higgs potential couplings. We find critical points with massless glueballs and/or massless monopoles, confinement without a mass gap, and tensionless domain walls. We describe the transitions between regimes with different patterns of gauge symmetry breaking, or, in the matrix model language, between solutions with a different number of cuts. The standard large Nc expansion is singular near the critical points, with domain walls tensions scaling as a fractional power of Nc. We argue that the critical points are four dimensional analogues of the Kazakov critical points that are commonly found in low dimensional matrix integrals. We define a double scaling limit that yields the exact tension of BPS two-branes in the resulting N=1, four dimensional non-critical string theory. D-brane states can be deformed continuously into closed string solitonic states and vice-versa along paths that go over regions where the string coupling is strong.Comment: 32 pages, 4 figures, 1 appendix; v2: typos corrected and the physical distinction between the fields z and S made clearer in section 4.4; v3: more typos correcte

Field Theories on the Poincar\'e Disk

The massive scalar field theory and the chiral Schwinger model are quantized on a Poincar\'e disk of radius $\rho$. The amplitudes are derived in terms of hypergeometric functions. The behavior at long distances and near the boundary of some of the relevant correlation functions is studied. The exact computation of the chiral determinant appearing in the Schwinger model is obtained exploiting perturbation theory. This calculation poses interesting mathematical problems, as the Poincar\'e disk is a noncompact manifold with a metric tensor which diverges approaching the boundary. The results presented in this paper are very useful in view of possible extensions to general Riemann surfaces. Moreover, they could also shed some light in the quantization of field theories on manifolds with constant curvature scalars in higher dimensions.Comment: 22 pages, Plain TeX+harvma