Customer Reviews

String Theory (Cambridge Monographs on Mathematical Physics) (Volume 2)

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Polchinski's book on string theory is a very well written book about the subject. Also, the problems given in the book are valuable for a further understanding. Using it together with the book by Green, Schwarz, Witten one will afterwards have indeed little problems understanding the papers on this subject. However one caveat: if one reads this book, he or she shoudl be always aware that this topic is still deeply a research subject and by no means settled like mechanics. If this is always kept in mind, then this book is of considerable help in understanding one of the current frontiers of physics.

This book picks up for Volume I left off. Supersymmetry is added to strings, more symmetries are presented, string theory phenomenology is described and many topics introduced in Volume I are developed in more detail. The quality is as good as it was in the previous volume and I think this book is essential reading for anyone attempting to master string theory.

The main addition in this volume is the expanded coverage of supersymmetry. In brief, the early chapter topics include the relation of worldsheet supersymmetry to spacetime supersymmetry, the various types of superstrings (I, IIA, IIB, and Heterotic) and even W-algebras. Calculations of critical dimensions, scattering amplitudes and anomaly cancellations are also done.

After incorporating supersymmetry into D-branes and T-duality (two concepts first introduced in the context of bosonic strings in Volume I), the text moves on to cover strings at strong coupling. It's a great chapter, my favorite of the book. Among the things covered are U-duality, black hole entropy, the black hole information paradox and M-theory.

After a chapter covering conformal field theory in more detail there are two chapters on compactification. One for orbifolds and one for Calabi-Yau spaces. The latter gives a nice overview of the techniques of complex geometry and algebraic topology needed to study Calabi-Yau spaces (there is also an appendix covering much of the math). Phenomenology is touched on in these, but it's in the following chapter that a more fully developed presentation of the possible string theory connection with the standard model and grand unified field theory is given. One thing I enjoyed was that in addition to string specific physics, this chapter discusses more general aspects of grand unified theories.

The final chapter contains a collection of advanced topics, with mirror symmetry being one of them.

To summarize this is a can't miss book for people seeking to understand string theory. Is anything missing? Not really, although more extensive coverage of black holes and D-branes would've been nice. It definitely left me wishing there was a Volume III on the horizon.

Reading this book is the easiest way to become familiar with various topics that seemed to be extremely difficult before. The reader then shouldn't have any problems with understanding current research papers.

In the second volume of the series the author generalizes the results of the first to string theories where supersymmetry is present. The mathematics introduced is non-rigorous, and the strategy is to see how much of the formalism for the bosonic case can be carried over to the case where fermions are present. The book is purely an exposition on the subject of string theory, and so no attempt is made to give the reader an in-depth explanation of the ideas and concepts in this area. This is particularly noticeable in the chapter on Calabi-Yau compactification and in the discussion on mirror symmetry in the last chapter. Here is a brief outline of the contents of the book:

- Generalize the mass-shell condition (Klein-Gordon equation in momentum space) by using the Dirac equation.

- The gamma matrices will serve as CM modes of an anticommuting world sheet field.

- The resulting world-sheet supercurrents generate the superconformal transformations of the superconformal algebra.

- Counting the number of (3/2, 0) currents classifies the different superconformal field theories.

- Standard quantization techniques for constrained systems are applied.

- Free SCFTs can be obtained with the vanishing of the central charge giving 10 as the critical dimension.

- SCFT on a circle gives two periodicity conditions for the matter fermions (Ramond and Neveu-Schwarz sectors).

- Ramond and Neveu-Schwarz algberas result. - Holomorphicity constraints give bosonization via the relation between the R sector vertex operators and bosonic winding state vertex operators.

- In 10 flat dimensions, 16 sectors result from the R and NS sectors, 6 of which are empty.

- Consistency conditions yield type IIA and IIB superstring theories.

- The vacuum amplitude for a closed superstring can be found by imposing modular invariance.

- Divergences cancell in the cylinder, Mobius strip, and Klein bottle graphs.

- Generalize preceding constructions by looking for sets of holomorphic and antiholomorphic currents whose Laurent coefficients form a closed algebra.

- Consider algebras that are different on the left- and right-moving sides of the closed string, obtaining the heterotic string.

- Setting the dimensions to be the same at each side and 32 left-moving spin-1/2 fields gives the SO(32) string.

- Split these fields into sets of 16 with independent boundary conditions to get the E8 X E8 heterotic string.

- Use supersymmetry constraints to study interactions of massless degrees of freedom.

- Tree-level interactions can be studied within low-energy supergravity; one-loop gives rise to anomalies.

- Anomalies cancell in type IIA, IIB, type I, and heterotic string theories.

- Use string perturbation theory to calculate amplitudes and interactions.

- Introduce supersymmetry in toroidally compactified string theory, to obtain D-branes which are BPS states and carry R-R charges.

- Type I, IIA, IIB string theories become states in a single theory.

- Study strongly coupled strings using D-brane states.

- The five string theories are limits of a single theory in 11-dimensional spacetime.

- Study conformal field theories as a prolegomena to analyzing string compactification.

- Study string compactification via free world-sheet conformal field theories or interacting exactly solvable conformal field theories.

- Connect the compactified string theory to the Standard Model.

- Start with orbifolds and then the more general Calabi-Yau manifolds.

- Techniques from algebraic geometry are brought in to study the properties of Calabi-Yau manifolds.

- Deduce an effective (low-energy) four-dimensional action using the topology of Calabi-Yau manifolds.

- Elaborate on the physics of four-dimensional string theory.

- Try to deal with the strong CP problem using Peccei-Quinn symmetry and the resulting axion field.

- Try to understand how gauge symmetries arise in the different string theories and how they are related to the ones in the Standard Model.

- Try to connect the different mass scales in string theory.

- Study more advanced topics in string theory, such as N = 2 superconformal algebras, type II superstrings on Calabi-Yau manifolds, string theories on the 4-dimensional Calabi-Yau manifold K3, minimal models, and mirror symmetry.

- Mirror manifolds can be constructed explicitly using Gepner models.

- Use mirror symmetry to obtain the full low energy field theory at the string tree level.

- Flop transitions can occur in string theory, giving dynamical changes in topology.