Membranes and Other Extendons ( p-branes)

Abstract

The physics of relativistic extended objects, or `extendons', as the authors term them, is a rapidly evolving sector of `hard' theoretical physics. One of the most intriguing aspects of this speculative field of research is to range over vastly different domains of physics, bridging the gap between micro and macro-cosmology. As a meaningful example, let us recall the almost ubiquitous role of strings in modern physics, since their first appearance in hadronic physics. Today, they are supposed to be the fundamental building blocks of the spacetime fabric itself. But linelike objects are also met as topological defects in superconductor physics, or as cosmic strings in cosmology. Moreover, it has been recently suggested that some basic mechanisms, ruling biological systems, can be formally described in terms of string and membrane dynamics as well. This book is a nice overview about the most recent developments in this active field of research. Reading this text is like reading a long scientific review article displayed in the editorial format of a `pocket-book'. A technical background knowledge in supersymmetric quantum field theory and differential geometry is a must, to follow the authors in their guided tour across the zoo of exotic extendons. Accordingly, the book may be particularly useful both for the expert researcher, looking for references and historical remarks, and for the PhD student looking for a brief, but exhaustive enough, introduction to the p-branes world. After opening with two historical chapters, the authors introduce the reader to the classical dynamics of bosonic extendons, and provide a detailed discussion of the several action functionals currently available in the literature. The two possible supersymmetric generalizations of the previously discussed bosonic models, i.e. `super-extendons' and `spinning extendons' are discussed in chapter 4. Specific models are considered in chapter 5, and a wide range of extended structures dominated, physical scenarios is plainly displayed. As the authors say, by scaling up many orders of magnitude, one can shift from hypothetical extended models of leptons down to the flexible, d = 2, fluid membrane and soap bubble. This is a nice example of the many roles extendons can play in vastly different physical frameworks. Chapter 6 faces the problem of quantizing, at least in a semiclassical way, such highly nonlinear objects. Chapter 7 is concerned with the group theoretical properties of extendons. Chapter 8 is devoted to the problem of embedding extended objects in curved spacetime. A special emphasis is due to the role of the embedding space critical dimensionality, and to the proper formulation of the fermionic frame fields required by supersymmetry. Finally, according to the style of the whole book, chapter 9 is a two-page long summary of the main results and of the current open problems.