Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux

We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct a set of finite-gap equations that describe the classical string spectrum. Using the recently proposed all-loop S-matrix we write down the all-loop Bethe ansatz equations for the massive sector. In the thermodynamic limit the Bethe ansatz reproduces the finite-gap equations. As part of this derivation we propose expressions for the leading order dressing phases. These phases differ from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure Ramond-Ramond case. We also consider the one-loop quantization of the algebraic curve and determine the one-loop corrections to the dressing phases. Finally we consider some classical string solutions including finite size giant magnons and circular strings.Comment: 44 pages, 3 figures. v2: references and a discussion about perturbative results adde

Free field realization of the exceptional current superalgebra \hat{D(2,1;\a)}_k

The free-field representations of the D(2,1;\a) current superalgebra and the corresponding energy-momentum tensor are constructed. The related screening currents of the first kind are also presented.Comment: Latex file, 10 page

On the dressing factors, Bethe equations and Yangian symmetry of strings on AdS3 × S3 × T4

Integrability is believed to underlie the AdS3/CFT2 correspondence with sixteen supercharges. We elucidate the role of massless modes within this integrable framework. Firstly, we find the dressing factors that enter the massless and mixed-mass worldsheet S matrix. Secondly, we derive a set of all-loop Bethe Equations for the closed strings, determine their symmetries and weak-coupling limit. Thirdly, we investigate the underlying Yangian symmetry in the massless sector and show that it fits into the general framework of Yangian integrability. In addition, we compare our S matrix in the near-relativistic limit with recent perturbative worldsheet calculations of Sundin and Wulff

Introduction

Reading through the articles in this Symposium is like walking deep into a dense forest. The experience is exhilarating but edged by a concern that the farther you go, the less sure you are of where you are. The articles here reveal the problem of cultural preservation in all its complexity and many-sidedness. This is not one of those symposia where the authors seek to outdo each other in self-condemnation for the wrongs perpetrated by colonial invaders on hapless indigenous people. Neither is it a lament for the assault on science by advocates of modish multiculturalism. The essays here are serious efforts to understand and to explore the implications of one important strand of the contemporary interest in communities as a focus for political, moral, and cultural life

An Environmental Common Law for Michigan

Extracts from testimony before the Committee on Conservation and Recreation, Michigan House of Representatives, on H. B. 3055, January 21 1970. The bill authorizes the Attorney General, local governments and private citizens to go to court and challenge activities which infring the right of the public to a clean, healthy, and attractive environment. Courts are empowered to take evidence in such cases and to enter orders prohibiting or modifying conduct that is shown to impair or threaten the quality of the environment. In 1969 the Western Michigan Environmental Action Council retained Professor Sax to draft a model environmental quality bill. H. B. 3055 incorporates the provisions of that model bill