Proceedings of a Summer Institute in Water Resources: Volume 4 - General Principles of Water Resources Planning

Foreward: Recognizing the need for training of individuals to meet the rapidly rising problems connected with water resources development, Utah State University, with National Science Foundation support, organized a Summer Institute in Water Resources for college teachers. it was hoped that participants carefully selected from all regions of the country would receive additional insight and stimulation to improve and enlarge water resources training programs at their own institutions. Thus, the accelerated dissemination of such knowledge on a national scale could be facilitated. Realizing further that the key to a successful institute of this nature lay in the excellence of its staff, efforts were made to obtain instructors with intimate knowledge and broad experience int he subject matter area they were asked to rpesent. In nearly every case those selected willingly accepted the invitation to participate, although this meant considerable monetary sacrifice and major adjustment of busy schedules. The subject matter treated paralleled regular offerings listed in the University catalog and is considered to be central or core to a water resources planning and management training program. one course treated the philosophical, historical, institutional, political, and legal aspects of water development. The responsibility for this course was shared jointly with Cleve H. Milligan, Charles E. Corker, and Wayne D. Criddle. The second course considered the principles of water resources economics and was presented by B. Delworth Gardner. The third course dealt with concepts of water quality management and was under the direction of P. H. McGauhey. The final course was on principles and procedures of regional resources planning and was presented jointly by Aaron Wiener, W. R. Derrick Sewell, and Harvey O. Banks. Having assembled a distinguished and diversified staff to present some of the best current professional thinking in the topics suggested in the preceding paragraph, it was felt most appropriate to attempt to put their lectures into writing. A proceedings of the Institute would have considerable utility beyong the Institute itself. Hence, the instructors were encouraged to prepare written material for the proceedings and were given secretarial and other assistance to aid them. This material has been organized according to the four major courses and is issued in four comanion volumes. Clearly, this has been a prodigious effort which required Institute staff and others to go the extra mile. Special thanks and recognition are due Mrs. Dorothy Riley who not only typed the entire proceedings but also attended to many details necessary for the successfult operations of the Institute. Jay M. Bagley served as director of the Institute and assumed a general coordinating and editing role in the development of these proceedings

Crossings, Motzkin paths and Moments

Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain $q$-analogues of Laguerre and Charlier polynomials. The moments of these orthogonal polynomials have combinatorial models in terms of crossings in permutations and set partitions. The aim of this article is to prove simple formulas for the moments of the $q$-Laguerre and the $q$-Charlier polynomials, in the style of the Touchard-Riordan formula (which gives the moments of some $q$-Hermite polynomials, and also the distribution of crossings in matchings). Our method mainly consists in the enumeration of weighted Motzkin paths, which are naturally associated with the moments. Some steps are bijective, in particular we describe a decomposition of paths which generalises a previous construction of Penaud for the case of the Touchard-Riordan formula. There are also some non-bijective steps using basic hypergeometric series, and continued fractions or, alternatively, functional equations.Comment: 21 page

Localized modes at a D-brane--O-plane intersection and heterotic Alice strings

We study a system of $N_c$ $D3$-branes intersecting $D7$-branes and $O7$-planes in 1+1-dimensions. We use anomaly cancellation and string dualities to argue that there must be chiral fermion zero-modes on the $D3$-branes which are localized near the $O7$-planes. Away from the orientifold limit we verify this by using index theory as well as explicit construction of the zero-modes. This system is related to F-theory on K3 and heterotic matrix string theory, and the heterotic strings are related to Alice string defects in $\mathcal{N}=4$ Super-Yang-Mills. In the limit of large $N_c$ we find an $AdS_3$ dual of the heterotic matrix string CFT.Comment: 44 pages, typos corrected, version published in JHE

Effective Action for Membrane Dynamics in DLCQ MM theory on a Two-torus

The effective action for the membrane dynamics on the background geometry of the $N$-sector DLCQ $M$ theory compactified on a two-torus is computed via supergravity. We compare it to the effective action obtained from the matrix theory, i.e., the (2+1)-dimensional supersymmetric Yang-Mills (SYM) theory, including the one-loop perturbative and full non-perturbative instanton effects. Consistent with the DLCQ prescription of $M$ theory {\em a la} Susskind, we find the precise agreement for the finite $N$-sector (off-conformal regime), as well as for the large $N$ limit (conformal regime), providing us with a concrete example of the correspondence between the matrix theory and the DLCQ $M$ theory. Non-perturbative instanton effects in the SYM theory conspire to yield the eleven-dimensionally covariant effective action.Comment: 11 pages, latex, no figure

DLCQ of Fivebranes, Large N Screening, and L^2 Harmonic Forms on Calabi Manifolds

We find one explicit L^2 harmonic form for every Calabi manifold. Calabi manifolds are known to arise in low energy dynamics of solitons in Yang-Mills theories, and the L^2 harmonic form corresponds to the supersymmetric ground state. As the normalizable ground state of a single U(N) instanton, it is related to the bound state of a single D0 to multiple coincident D4's in the non-commutative setting, or equivalently a unit Kaluza-Klein mode in DLCQ of fivebrane worldvolume theory. As the ground state of nonabelian massless monopoles realized around a monopole-``anti''-monopole pair, it shows how the long range force between the pair is screened in a manner reminiscent of large N behavior of quark-anti-quark potential found in AdS/CFT correspondence.Comment: LaTeX, 23 page

Orientifolds, RG Flows, and Closed String Tachyons

We discuss the fate of certain tachyonic closed string theories from two perspectives. In both cases our approach involves studying directly configurations with finite negative tree-level cosmological constant. Closed string analogues of orientifolds, which carry negative tension, are argued to represent the minima of the tachyon potential in some cases. In other cases, we make use of the fact, noted in the early string theory literature, that strings can propagate on spaces of subcritical dimension at the expense of introducing a tree-level cosmological constant. The form of the tachyon vertex operator in these cases makes it clear that a subcritical-dimension theory results from tachyon condensation. Using results of Kutasov, we argue that in some Scherk-Schwarz models, for finely-tuned tachyon condensates, a minimal model CFT times a subcritical dimension theory results. In some instances, these two sets of ideas may be related by duality.Comment: 15 pages, 2 figures, uses harvmac; v2: references adde

Closed-String Tachyons and the Hagedorn Transition in AdS Space

We discuss some aspects of the behaviour of a string gas at the Hagedorn temperature from a Euclidean point of view. Using AdS space as an infrared regulator, the Hagedorn tachyon can be effectively quasi-localized and its dynamics controled by a finite energetic balance. We propose that the off-shell RG flow matches to an Euclidean AdS black hole geometry in a generalization of the string/black-hole correspondence principle. The final stage of the RG flow can be interpreted semiclassically as the growth of a cool black hole in a hotter radiation bath. The end-point of the condensation is the large Euclidean AdS black hole, and the part of spacetime behind the horizon has been removed. In the flat-space limit, holography is manifest by the system creating its own transverse screen at infinity. This leads to an argument, based on the energetics of the system, explaining why the non-supersymmetric type 0A string theory decays into the supersymmetric type IIB vacuum. We also suggest a notion of `boundary entropy', the value of which decreases along the line of flow.Comment: 24 pages, Harvmac. 2 Figures. Typos corrected and reference adde

Lectures on Non-BPS Dirichlet branes

A comprehensive introduction to the boundary state approach to Dirichlet branes is given. Various examples of BPS and non-BPS Dirichlet branes are discussed. In particular, the non-BPS states in the duality of Type IIA on K3 and the heterotic string on T4 are analysed in detail.Comment: 46 pages, 5 figures, LaTeX; lectures given at the TMR network school on `Quantum aspects of gauge theories, supersymmetry and quantum gravity', Torino, 26 January - 2 February 2000, and at the `Spring workshop on Superstrings and related matters', Trieste, 27 March - 4 April 2000; references adde

Duality Twists, Orbifolds, and Fluxes

We investigate compactifications with duality twists and their relation to orbifolds and compactifications with fluxes. Inequivalent compactifications are classified by conjugacy classes of the U-duality group and result in gauged supergravities in lower dimensions with nontrivial Scherk-Schwarz potentials on the moduli space. For certain twists, this mechanism is equivalent to introducing internal fluxes but is more general and can be used to stabilize some of the moduli. We show that the potential has stable minima with zero energy precisely at the fixed points of the twist group. In string theory, when the twist belongs to the T-duality group, the theory at the minimum has an exact CFT description as an orbifold. We also discuss more general twists by nonperturbative U-duality transformations.Comment: 30 pages, harvmac, references and brief comments on gauged supergravity adde

Closed String Tachyon Condensation: An Overview

These notes are an expanded version of a review lecture on closed string tachyon condensation at the RTN workshop in Copenhagen in September 2003. We begin with a lightning review of open string tachyon condensation, and then proceed to review recent results on localized closed string tachyon condensation, focusing on two simple systems, C/Z_n orbifolds and twisted circle compactifications.Comment: harvmac, 59 pages; references adde