Superstring Theory: Volume 1, Introduction (Cambridge Monographs on Mathematical Physics)

Rating:
Summary: Should still be required reading
Review: Anyone interested in learning string theory could perhaps start with the current formulation involving D-branes and M theories. This is certainly possible and will lead one to the frontiers of research. However, it would not perhaps give one an appreciation of string theory that would be obtained by persuing a study that explains how it arose in the study of the strong interaction . This book, written by three giants in string theory, will give the reader such a study, and was the first book to appear on the subject. The book is a monograph, and not a textbook, since no exercises appear, but it could still serve as a reference and "required reading" for courses in string theory.

The learning of string theory can be a formidable undertaking for those who lack the mathematical background. Indeed, a proper understanding of string theory, not just a forma one, will require a solid understanding of algebraic and differential geometry, algebraic topology, and complex manifolds. There are many books on these subjects, but I do not know of one what will give the student of string theory an in-depth understanding of the relevant mathematics. These two volumes include two rather lengthy chapters on mathematics, one on differential geometry and the other on algebraic geometry. The mastery of these two chapter will give readers a formal understanding of the mathematics, and will allow them to perform calculations in string theory efficiently, but do not give the insight needed for extending its frontiers. There have been a few books published on string theory since these two volumes appeared, but they too fail in this regard (and some even admit to doing so). To gain the necessary insight into the mathematics will entail a very time-consuming search of the early literature and many face-to-face conversations with mathematicians. The "oral tradition" in mathematics is real and one must embed onself in it if a real, in-depth understanding of mathematics is sought.

The physics of string theory though is brought out with incredible skill by the authors, and the historical motivation given in the introduction is the finest in the literature. Now legendary, the origin of string theories in the dual models of the strong interaction is discussed in detail. The Veneziano model, as discussed in this part, has recently become important in purely mathematical contexts, as has most every other construction in string theory. The mathematical results that have arisen from string theory involves some of the most fascinating constructions in all of mathematics, and mathematicians interested in these will themselves be interested in perusing these volumes, but will of course find the approach mathematically non-rigorous.

Some of the other discussions that stand out in the book include: 1. The global aspects of the string world sheet and the origin of the moduli space, along with its connection to Teichmuller space. 2. The world-sheet supersymmetry and the origin of the integers 10 and 26 as being a critical dimension. In this discussion, the authors give valuable insight on a number of matters, one in particular being why the introduction of an anticommuting field mapping bosons to bosons and fermions to fermions does not violate the spin-statistics theorem. 3. The light-cone gauge quantization for superstrings. The authors show that the manifestly covariant formalism is equivalent to the light-cone formalism and is ghost-free in dimension 10. The light-cone gauge is used to quantize a covariant world-sheet action with space-time supersymmetry, with this being Lorentz invariant in dimension 10. This allows, as the authors explain in lucid detail, the unification of bosonic and fermionic strings in a single Fock space. 4. Current algebra on the string world sheet and its origin in the need for distributing charge throughout the string, rather than just at the ends. The origin of heterotic string theory is explained in this context.

Rating:
Summary: Still worth the effort
Review: While the subject of string theory has undergone considerable and radical change since publication of this text and since Polchinski's recent texts takes some of the steam out of this title, overall it remains a relevant part of the literature for a number of reasons. First, vol I clearly serves a vital role as a secondary source to both of Polchinski's text and vice versa: Polchinski's vol's I&II update Green / Schwarz / Witten's (GSW) vol I. Whereas Polichinski's vol I focuses exclusively on the bosonic strings GSW vol I includes both supersymmetric & bosonic string theory. A reader can then go along way on joining vol I of Polchinski and vol I of GSW.

But probably the greatest reason to purchase this title is the insight into string theory that is offered by these particular authors --- individuals who have each served as principle architects of string theory since its inception and through its many revolutions.

In general, the prose is congenial as is the level of sophistication in physical and mathematical argument. The mathematical apparatus of string theory can become very heavy very quickly and these authors orient the reader in that difficult terrain in a truly adroit fashion.

Rating:
Summary: Still the best
Review: Why I still recommend this book rather than Polchinski's book is because this book presents more motivation and physics of string theory. In the 90s, there was string duality revolution, a side-effect of which is that string theorists neglect experiments.