Alfred D. Shapere

Geometric Phases in Physics

During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as ‘Berrys phase’) in addition to the usual dynamical phase derived from Schrodingers equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified and found to be important in a startling variety of physical contexts, ranging from nuclear magnetic resonance and low-Reynolds number hydrodynamics to quantum field theory. This volume is a collection of original papers and reprints, with commentary, on the subject.

The Coulomb phase of N=2 supersymmetric QCD

We present an explicit nonperturbative solution of N=2 supersymmetric SU({ital N}) gauge theory with {ital N}{sub {ital f}}{le}2{ital N} flavors generalizing results of Seiberg and Witten for {ital N}=2.

Self-dual models with theta terms

Il existe une large classe de modeles qui sont autoduaux par rapport a linversion des constantes de couplage. Quand on ajoute un terme theta, cette dualite peut etre etendue a une invariance par rapport a une action dun groupe modulaire discret infini sur lespace des parametres de couplage. En particulier, les theories de jauge reticulaires abeliennes a 4 dimensions possedent une symetrie modulaire Sp (2k, Z), ou k est le nombre des facteurs simples dans le groupe de jauge. On generalise ce resultat aux modeles de dimension arbitraire et on montre que les fonctions de partition des modeles de spin Z N bidimensionnels avec 2 k flaveurs et compactification de corde sur des tores k-dimensionnels, sont invariantes par rapport a O (k, k; Z). On trace aussi quelques paralleles suggestifs a leffet Hall quantique fractionnaire

Black hole production by cosmic rays

Ultrahigh energy cosmic rays create black holes in scenarios with extra dimensions and TeV-scale gravity. In particular, cosmic neutrinos will produce black holes deep in the atmosphere, initiating quasihorizontal showers far above the standard model rate. At the Auger Observatory, hundreds of black hole events may be observed, providing evidence for extra dimensions and the first opportunity for experimental study of microscopic black holes. If no black holes are found, the fundamental Planck scale must be above 2 TeV for any number of extra dimensions.

Limitations on the statistical description of black holes

We argue that the description of a block hole as a statistical (thermal) object must break down as the extreme (zero-temperature) limit is a approached, due to uncontrollable thermodynamic fluctuatations. For the recently discovered charged black holes, the analysis is significantly different, but again indicates that a statistical decription of the extreme hole is inappropriate. These holes invite a more normal elementary particle interpretation than is possible for Reissner-Nordstrom hole.

DUAL DILATION DYONS

We find four-dimensional black hole solutions of the tree-level string effective action, that carry both electric and magnetic charge. The solutions involve non-trivial axion and dilaton fields, and are related to one another by a form of duality transformation. These black holes have drastically different global properties from the usual charged holes without axions and dilatons. The global causal structures of the effective metrics seen by different types of particles (for the same solution) can differ.

Gauge kinematics of deformable bodies

The treatment of the motion of deformable bodies requires a specification of axes for each shape. A natural kinematic formulation of this problem is presented in terms of a gauge structure over the space of shapes that the body may assume. Within this framework, one may compute the net change in orientation of a body with angular momentum zero, resulting from a given sequence of deformations.

A counterexample to the a-`theorem'

We exhibit a renormalization group flow for a four-dimensional gauge theory along which the conformal central charge a increases. The flow connects the maximally superconformal point of an = 2 gauge theory with gauge group SU(N+1) and Nf = 2N flavors in the ultraviolet, to a strongly-coupled superconformal point of the SU(N) gauge theory with Nf = 2N massless flavors in the infrared. Our example does not contradict the proof of the a-theorem via a-maximization, due to the presence of accidental symmetries in the infrared limit. Nor does it contradict the holographic a-theorem, because these gauge theories do not possess weakly-curved holographic duals.

Gauge symmetries of the N=2 string

Abstract We study the underlying gauge symmetry algebra of the N = 2 string, which is broken down to a subalgebra in any spacetime background. For given toroidal backgrounds, the unbroken gauge symmetries (corresponding to holomorphic and antiholomorphic worldsheet currents) generate area-preserving diffeomorphism algebras of null 2-tori. A minimal Lie algebraic closure, containing all the gauge symmetries that arise in this way, is the background-independent volume-preserving diffeomorphism algebra of the target Narain torus T4,4. The underlying symmetries act on the ground ring of functions on T4,4 as derivations, much as in the case of the d = 2 string. A background-independent spacetime action valid for noncompact metrics is presented, whose symmetries are volume-preserving diffeomorphisms. Possible extensions to N = 2 and N = 1 heterotic strings are briefly discussed.

Solitons, Duality, and Supersymmetric Gauge Theories

Some aspects of solitons in supersymmetric gauge theories are reviewed, with particular attention to the roles played by solitons in the realization of duality transformations and the physical effects of massless solitons.