Boundary changing operators in the O(n) matrix model

We continue the study of boundary operators in the dense O(n) model on the random lattice. The conformal dimension of boundary operators inserted between two JS boundaries of different weight is derived from the matrix model description. Our results are in agreement with the regular lattice findings. A connection is made between the loop equations in the continuum limit and the shift relations of boundary Liouville 3-points functions obtained from Boundary Ground Ring approach.Comment: 31 pages, 4 figures, Introduction and Conclusion improve

Hydrogeologic Conditions Around Deep Aeration Lagoons at the Bardstown Wastewater Treatment Plant

The hydrogeologic conditions around the Bardstown Sewage Treatment Plant were studied from August 1996 through December 1997. Hydraulic and geochemical data were collected from eight monitoring wells and four surface-water monitoring sites on the plant property. There is a large hydraulic gradient between the lagoons at the plant and the surrounding stream, Town Creek. Initial water-level measurements in wells surrounding the site suggest no major leakage from the lagoons, however. Neither flowing artesian conditions nor unusually high water levels were observed in any of the wells. Water-level measurements collected by data loggers showed that shallow wells responded quickly to recharge, whereas bedrock wells were relatively unresponsive throughout most of the observation period. Slug tests indicate that the hydraulic conductivities of the unconsolidated material monitored by the shallow wells are several orders of magnitude greater than for the underlying bedrock. Surface-water flow measurements indicate that Town Creek is a losing stream adjacent to the lagoons. This conclusion is supported by hydraulic data from the monitoring wells. These data suggest that it is unlikely the lagoons are leaking significantly into Town Creek. Town Creek appears to become a gaining stream along its lowest reaches on the northwestern side of the plant property. Interpretation of chloride, bromide, fluoride, and major-ion chemistry data indicates that the water chemistry in the shallow wells is not affected significantly by the lagoons. Well-water chemistry is influenced by Town Creek, which recharges the shallow alluvial sediments during high flow. All metal concentrations appear to be below primary and secondary maximum contaminant levels (MCL\u27s) in both the lagoons and the stream water. The only metals for which the MCL was exceeded at the site are iron and manganese; concentrations were relatively high in the shallow ground-water monitoring wells. Concentrations of these metals are commonly elevated in ground water derived from shallow, alluvial sediments in this physiographic region, however. These data suggest that the lagoons are having a minimal impact, if any, on the quality of ground water around the lagoons. The results from a one-time sampling for bacteria indicate that the total coliform in the monitoring wells ranged from 10 to 1,920 colonies per 100 ml (col/100 ml). Analysis for E. coli bacteria showed that only one well, BT30, contained measurable counts (10 col/100 ml). The presence of E. coli in this well is inconsistent with other parameters that would indicate contamination from the lagoons, however; their presence may represent contamination during sampling. The data from this investigation, as well as previous studies, indicate that the lagoons provide efficient primary water treatment without causing significant ground-water contamination. Moreover, the design and engineering used for the Bardstown plant may provide a model for cost-effective, efficient primary water-treatment systems capable of long-term operation without affecting the local ground-water system. Lagoons in other physiographic and geologic settings should be studied to determine the effect of large lagoons throughout the state. This is especially pertinent now, because public and regulatory agencies have expressed great interest in lagoon technology for managing wastes from large-scale livestock operations

Nonperturbative Effects from the Resummation of Perturbation Theory

Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect we argue that the nonperturbative effect associated with the perturbation theory should have a branch cut only along the positive real axis in the complex coupling plane. The component in the weak coupling expansion of the nonperturbative amplitude, which usually includes the leading term in the weak coupling expansion, that gives rise to the branch cut can be calculated in principle from the perturbation theory combined with some exactly calculable properties of the nonperturbative effect. The realization of this mechanism is demonstrated in the double well potential and the two-dimensional O(N) nonlinear sigma model. In these models the leading term in weak coupling of the nonperturbative effect can be obtained with good accuracy from the first terms of the perturbation theory. Applying this mechanism to the infrared renormalon induced nonperturbative effect in QCD, we suggest some of the QCD condensate effects can be calculated in principle from the perturbation theory.Comment: 21 Pages, 1 Figure; To appear in Phys Rev

Phenomenology of the Gowdy Universe on T3×RT^3 \times R

Numerical studies of the plane symmetric, vacuum Gowdy universe on $T^3 \times R$ yield strong support for the conjectured asymptotically velocity term dominated (AVTD) behavior of its evolution toward the singularity except, perhaps, at isolated spatial points. A generic solution is characterized by spiky features and apparent ``discontinuities'' in the wave amplitudes. It is shown that the nonlinear terms in the wave equations drive the system generically to the ``small velocity'' AVTD regime and that the spiky features are caused by the absence of these terms at isolated spatial points.Comment: 19 pages, 21 figures, uses Revtex, psfi

Generalized Penner models to all genera

We give a complete description of the genus expansion of the one-cut solution to the generalized Penner model. The solution is presented in a form which allows us in a very straightforward manner to localize critical points and to investigate the scaling behaviour of the model in the vicinity of these points. We carry out an analysis of the critical behaviour to all genera addressing all types of multi-critical points. In certain regions of the coupling constant space the model must be defined via analytical continuation. We show in detail how this works for the Penner model. Using analytical continuation it is possible to reach the fermionic 1-matrix model. We show that the critical points of the fermionic 1-matrix model can be indexed by an integer, $m$, as it was the case for the ordinary hermitian 1-matrix model. Furthermore the $m$'th multi-critical fermionic model has to all genera the same value of $\gamma_{str}$ as the $m$'th multi-critical hermitian model. However, the coefficients of the topological expansion need not be the same in the two cases. We show explicitly how it is possible with a fermionic matrix model to reach a $m=2$ multi-critical point for which the topological expansion has alternating signs, but otherwise coincides with the usual Painlev\'{e} expansion.Comment: 27 pages, PostScrip

CHL Dyons and Statistical Entropy Function from D1-D5 System

We give a proof of the recently proposed formula for the dyon spectrum in CHL string theories by mapping it to a configuration of D1 and D5-branes and Kaluza-Klein monopole. We also give a prescription for computing the degeneracy as a systematic expansion in inverse powers of charges. The computation can be formulated as a problem of extremizing a duality invariant statistical entropy function whose value at the extremum gives the logarithm of the degeneracy. During this analysis we also determine the locations of the zeroes and poles of the Siegel modular forms whose inverse give the dyon partition function in the CHL models.Comment: LaTeX file, 48 pages; v2: typos correcte

Loop Gas Model for Open Strings

The open string with one-dimensional target space is formulated in terms of an SOS, or loop gas, model on a random surface. We solve an integral equation for the loop amplitude with Dirichlet and Neumann boundary conditions imposed on different pieces of its boundary. The result is used to calculate the mean values of order and disorder operators, to construct the string propagator and find its spectrum of excitations. The latter is not sensible neither to the string tension \L nor to the mass $\mu$ of the ``quarks'' at the ends of the string. As in the case of closed strings, the SOS formulation allows to construct a Feynman diagram technique for the string interaction amplitudes

Generalized Kac-Moody Algebras from CHL dyons

We provide evidence for the existence of a family of generalized Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for (N,k)=(1,10), (2,6), (3,4), and possibly (5,2). The square of the automorphic form is the modular transform of the generating function of the degeneracy of CHL dyons in asymmetric Z_N-orbifolds of the heterotic string compactified on T^6. The new generalized Kac-Moody superalgebras all arise as different `automorphic corrections' of the same Lie algebra and are closely related to a generalized Kac-Moody superalgebra constructed by Gritsenko and Nikulin. The automorphic forms, Delta_{k/2}(Z), arise as additive lifts of Jacobi forms of (integral) weight k/2 and index 1/2. We note that the orbifolding acts on the imaginary simple roots of the unorbifolded GKM superalgebra, G_1 leaving the real simple roots untouched. We anticipate that these superalgebras will play a role in understanding the `algebra of BPS states' in CHL compactifications.Comment: LaTeX, 35 pages; v2: improved referencing and discussion; typos corrected; v3 [substantial revision] 44 pages, modularity of additive lift proved, product representation of the forms also given; further references adde

TeV Astrophysics Constraints on Planck Scale Lorentz Violation

We analyze observational constraints from TeV astrophysics on Lorentz violating nonlinear dispersion for photons and electrons without assuming any a priori equality between the photon and electron parameters. The constraints arise from thresholds for vacuum Cerenkov radiation, photon decay and photo-production of electron-positron pairs. We show that the parameter plane for cubic momentum terms in the dispersion relations is constrained to an order unity region in Planck units. We find that the threshold configuration can occur with an asymmetric distribution of momentum for pair creation, and with a hard photon for vacuum Cerenkov radiation.Comment: 4 pages, RevTeX4, 1 figure. Some references and a footnote added, improved discussion on the photon annihilation and GZK cutoff. Minor changes of wording. Main results unchanged. Version to appear as a Rapid Communication in PR

Noncommutative probability, matrix models, and quantum orbifold geometry

Inspired by the intimate relationship between Voiculescu's noncommutative probability theory (of type A) and large-N matrix models in physics, we look for physical models related to noncommutative probability theory of type B. These turn out to be fermionic matrix-vector models at the double large-N limit. In the context of string theory, they describe different orbifolded string worldsheets with boundaries. Their critical exponents coincide with that of ordinary string worldsheets, but their renormalised tree-level one-boundary amplitudes differ.Comment: 22 pages, 8 eps figures, LaTeX2.09; title changed, mistakes correcte