String Theory and M-Theory: A Modern Introduction [Hardcover]

Katrin Becker (Author), Melanie Becker (Author), John H. Schwarz (Author)

Book Description

ISBN-10: 0521860695 | ISBN-13: 978-0521860697 | Publication Date: January 15, 2007 | Edition: 1

String theory is one of the most exciting and challenging areas of modern theoretical physics. This book guides the reader from the basics of string theory to recent developments. It introduces the basics of perturbative string theory, world-sheet supersymmetry, space-time supersymmetry, conformal field theory and the heterotic string, before describing modern developments, including D-branes, string dualities and M-theory. It then covers string geometry and flux compactifications, applications to cosmology and particle physics, black holes in string theory and M-theory, and the microscopic origin of black-hole entropy. It concludes with Matrix theory, the AdS/CFT duality and its generalizations. This book is ideal for graduate students and researchers in modern string theory, and will make an excellent textbook for a one-year course on string theory. It contains over 120 exercises with solutions, and over 200 homework problems with solutions available on a password protected website for lecturers at www.cambridge.org/9780521860697.

Editorial Reviews

Review

"This is the first comprehensive textbook on string theory to also offer an up-to-date picture of the most important theoretical developments of the last decade, including the AdS/CFT correspondence and flux compactifications, which have played a crucial role in modern efforts to make contact with experiment. An excellent resource for graduate students as well as researchers in high-energy physics and cosmology."
Nima Arkani-Hamed, Harvard University

"An exceptional introduction to string theory that contains a comprehensive treatment of all aspects of the theory, including recent developments. The clear pedagogical style and the many excellent exercises should provide the interested student or researcher a straightforward path to the frontiers of current research."
David Gross, Director of the Kavli Institute for Theoretical Physics, University of California, Santa Barabara and winner of the Nobel Prize for Physics in 2004

"Masterfully written by pioneers of the subject, comprehensive, up-to-date and replete with illuminating problem sets and their solution, String Theory and M-theory: A Modern Introduction provides an ideal preparation for research on the current forefront of the fundamental laws of nature. It is destined to become the standard textbook in the subject."
Andrew Strominger, Harvard University

"This book is a magnificcent resource for students and researchers alike in the rapidly evolving field of string theory. It is unique in that it is targeted for students without any knowledge of string theory and at the same time it includes the very latest developments of the field, all presented in a very fluid and simple form. The lucid description is nicely complemented by very instructive problems. I highly recommend this book to all researchers interested in the beautiful field of string theory."
Cumrun Vafa, Harvard University

"This elegantly written book will be a valuable resource for students looking for an entryway to the vast and exciting topic of string theory. The authors have skillfully made a selection of topics aimed at helping the beginner get up to speed. I am sure it will be widely read."
Edward Witten, Institute for Advanced Study, Princeton and winner of the Fields Medal in 1990

"A welcome addition to the literature and most likely will be the required text for those physicists who intend to study the many facets of this fascinating subject... String Theory and M-Theory is THE string textbook."
Pierre Ramond, University of Florida, Gainesville, Physics Today


"... a beautiful description of almost all the questions in the field that have been answered so far and those that are still open. The reader of the book gets a good picture of the current state of string theory..."
Marcel L. Vonk, Johannesburg, Mathematical Reviews

Book Description

This book guides the reader through string theory, one of the most exciting and challenging areas of modern theoretical physics. It is ideal for graduate students and researchers in modern string theory, and will make an excellent textbook. It contains exercises with solutions, and homework problems with solutions.

See all Editorial Reviews

Product Details

• Hardcover: 756 pages
• Publisher: Cambridge University Press; 1 edition (January 15, 2007)
• Language: English
• ISBN-10: 0521860695
• ISBN-13: 978-0521860697
• Product Dimensions: 9.9 x 7.1 x 1.5 inches
• Shipping Weight: 3.9 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (10 customer reviews)
• Amazon Best Sellers Rank: #612,705 in Books (See Top 100 in Books)

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28 of 29 people found the following review helpful:

5.0 out of 5 stars Excellent Book, March 10, 2007

By 

Dean Welch - See all my reviews
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This review is from: String Theory and M-Theory: A Modern Introduction (Hardcover)

I think this is a great book that provides not only a great introduction to string theory (there is no assumed prior knowledge of string theory), but also provides coverage of many more advanced topics as well. I think it's likely that the vast majority of students specializing in string theory will want to read it at some point in their studies.

The coverage of topics in the first few chapters is in some ways fairly standard. The first two chapters consists of a high level overview of string theory, bosonic string, the Nambu-Goto action the Polyakov action, the Virasoro algebra, the critical dimension, light code gauge and the spectra of open/closed strings. After this there is a chapter on conformal field theory, naturally emphasizing the parts relevant to string theory (including a bit of string field theory). This is followed by discussions of worldsheet supersymmetry, spacetime supersymmetry, anomalies, T-duality and heterotic strings. The writing is very clear and considering the nature of the material, fairly straight forward. There are two things that I considered exceptional strengths. One is that the discussions incorporate D-branes, M-theory and the (unexpected) symmetries of string theory early on. The other is that there are numerous worked examples, as there are throughout the book.

At a very high level the rest of the book contains more extensive discussions of M-theory, compactification (including a substantial amount besides the standard approach of the compact dimensions being a Calabi-Yau space), mirror symmetry, S-duality, possible cosmological consequences of string theory, black holes and other solutions with horizons, matrix theory, AdS/CFT correspondence (a proposed equivalence between closed string solutions on the product of a sphere and anti-deSitter space and Yang-Mills theories) and the holographic principle (or as some would say conjecture).

The things I appreciated the most about this material was that is was a very interesting mix of topics. The discussion of black holes and cosmology was fairly extensive (for cosmology it was the most extensive I've seen in a text book). As was the coverage of the AdS/CFT correspondence. There were also some topics that I don't recall seeing in other string theory books, such as warped geometries in compactification and S-branes (these are like D-branes but they satisfy Dirichlet boundary conditions in timelike directions).

Needless to say it's a fairly advanced book. There is some coverage of things like complex spaces, topology, general relativity and cosmology. However this material is more along the lines of a review, not something intended to teach from first principles (some of the other string theory books cover this kind material in more detail).

All-in-all I believe this book not only provides a great introduction, it also provides an excellent treatment of some of the more advanced topics in string theory.

42 of 46 people found the following review helpful:

4.0 out of 5 stars Best of All Worlds, March 9, 2007

By 

Cybertronian (Finland) - See all my reviews

This review is from: String Theory and M-Theory: A Modern Introduction (Hardcover)

This new textbook on string theory might be considered a modern pimped up version of Zwiebach's introductory course. The book is - as an introduction - better than the 2-volume set by Schwarz (Green, Schwarz, Witten), which is partly outdated, and on the same footing as Polchinski's version, but certainly not as thorough and elaborate. There is some overlap between all books (e.g. the CFT bits from Polchinski are quite similar to those in this new text, the introduction of the bosonic string via the relativistic point particle looks like the ones by Polchinski and Zwiebach, but Becker & Schwarz immediately generalise the concept to p-branes, SCFTs are discussed in a similar manner as in Polchinski, and so on), but there are additional features that really add to the value of the book: all exercises within the text have solutions directly under them, so one can either try to solve them or read them through, and some parts are explained more clearly. The concepts of "(gauge) symmetries" are discussed slightly better than by Polchsinki or GSW, but for those who want mathematical proofs instead of hand-waving arguments, and more background material on supersymmetry, I can only say that I have found no books on string theory that really do that. Both are subjects of study on their own and would go "beyond the scope" of these books... Nevertheless, a very good introduction and most of all: up to date!

For mid-undergraduates, I think, the perfect sequence for string theory would be (provided one acquires knowledge of QFT and Lie algebras for the more advanced texts):

Zwiebach>Becker/Schwarz>Polchinski (supplemented by GSW's first volume)

But if you want to learn string theory more quickly or if you don't have problems with the very basics, then leave out Zwiebach and go for this one immediately. For graduates, Polchinski should be the start, but one can take Backer/Schwarz always as a references and supplement on some topics (connection to black holes and gauge theories).

22 of 30 people found the following review helpful:

4.0 out of 5 stars A good general introduction, April 21, 2007

By 

Dr. Lee D. Carlson (Baltimore, Maryland USA) - See all my reviews
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This review is from: String Theory and M-Theory: A Modern Introduction (Hardcover)

String theory has been criticized since it was first invented but not to the degree that it has now, this criticism mostly focusing on its failure to connect with observation. The criticism has increased dramatically in recent years however, and some of this has been too vituperative to be useful to those curious about string theory as a viable physical theory. But criticism, however harsh, can be healthy, since it motivates the proponents of a theory to more carefully elucidate its foundations and content. This is usually not the case when a theory is popular, as researchers are in a competitive spirit and are hesitant to share the knowledge to possible competitors. At this stage in the game however, string theorists it seems are now on the defensive, and have thus taken the time to discuss in-depth what this reviewer still believes is the most complex and beautiful theory ever constructed in mathematical physics. String theory still has a long way to go before it gains status as being a physical theory, but hopefully by the end of the next few decades one will see the appearance of charts, graphs, and numerical calculations in books on string theory, much like one finds in the most successful of all physical theories to date: relativistic quantum field theory.
Some highlights in the book that are particularly insightful include:
1. The observation that Dirichlet boundary conditions (for the open string) break Poincare invariance, but that this leads to the introduction of Dp-branes as positions of the endpoints of the open string. Poincare invariance is recovered as long as Dp-brane is space filling, i.e. has a dimension one less than the background spacetime.
2. The view that the BRST quantization of the path integral is really a conformal field theory. This is interesting in that BRST analysis is typically thought of as a procedure for quantizing constrained systems (gauge theories being predominant examples).
3. The `Myers effect'. Sometimes referred to as the `D-brane dielectric effect', it is part of an attempt to understand the physics of non-Abelian D-branes for strong fields. One of the challenges in this understanding involves the validity of the Dirac-Born-Infeld action in these kinds of circumstances, which as the authors remark is designed for situations where the background fields and world-volume gauge fields do not vary appreciably over the distances on the order of the string scale.
4. The origin of the (classical) Virasoro algebra as the freedom of choice of gauge in the reparametrization symmetry. And along these same lines, the quantization of the Virasoro algebra is defined to the normal ordering of the Virasoro generators, and their commutators give an expression consisting of the ordinary classical term plus a "quantum" correction, the famous central extension. Thus the quantum Virasoro algebra can be viewed as a "quantum deformation" of the classical Virasoro algebra, with the central parameter as being the deformation parameter. This philosophy of deformation has found generalization in what are now called `quantum groups' (even though strictly speaking they are much more complicated objects than ordinary groups).
5. The connection of the dilaton to the Euler characteristic.
6. The role of the GSO projection in insuring consistency in the state spectrum.
7. The use of (vector bundle) K-theory to classify D-brane charges. This use arises when it is realized that the conserved R-R charges cannot be identified with cohomology classes of gauge field configurations. Instead, the D-branes are classified by K-theory classes.
8. The discussion on `primitive cohomology' and its relation to de Rham cohomology and Hodge theory.
9. The role of the Born-Infeld structure in ensuring Lorentz invariance of the T-dual description. The Born-Infeld action was once viewed as a mere historical curiosity, namely as a nonlinear generalization of the Maxwell theory, with no experimental backing. That it finds such a natural place in string theory is very interesting (but still of course lacking in experimental support).
10. The derivation of a lower bound for Newton's constant from heterotic M-theory, which is close to the observed value.
11. The argument, beautifully elucidated in this book, that type IIA supergravity may be obtained from 11-dimensional supergravity by dimensional reduction.
12. The discussion on warped space-times and the gauge hierarchy. The authors cleverly motivate this subject by asking why Newtonian gravity follows an inverse-square law rather than an inverse-cube law.
13. An entire chapter is devoted to "stringy" geometry, which is a fascinating subject given that it touches so many areas of modern mathematics.
14. The discussion of the `hidden sector' and its conjectured relation to dark matter and supersymmetry breaking.
15. The author's treatment of the AdS/CFT conjecture is superb and is by far the most interesting part of the book. The dualities shown to exists between gauge theory and string theory are a possible route to a full understanding of nonperturbative quantum chromodynamics, which to this date has defied resolution.

Some major omissions or discussions that need more elaboration include:
1. The difficulties that are actually involved in quantizing the Nambu-Goto action. The authors remark that this is due to the presence of the square root, but it would have been interesting if they would have indicated just where the trouble rises explicitly when a quantization procedure is attempted with the Nambu-Goto action. In ordinary quantum field theory, the presence of the square root is interpreted as a "nonlocal" problem, but even there this issue is not usually dealt with in a manner that is very transparent.
2. A more detailed treatment of string field theory for those readers who want to compare it to what is done in second quantization in ordinary quantum field theory.
3. The role of the Beltrami differentials in the attaining of a measure for moduli space that is invariant under reparametrizations of the moduli space.
4. No in-depth discussion of characteristic classes over and above the algebra involved in their manipulation (i.e. the wedge products). An understanding of characteristic classes is crucial to understanding superstring and brane theory, but the pages of this book mislead the unsuspecting reader that there is nothing to characteristic classes except algebraic manipulation of the differential forms. But characteristic classes have a deep geometrical meaning, and obtaining insight into this meaning has been proven to be difficult for students of string theory. This book does not provide any of this insight, nor do any of the other books currently in print on string theory.
5. Is supersymmetry absolutely necessary for the incorporation of fermions into string theory? The authors seem to argue that it is, but an explicit proof is lacking.
6. The proof that `threshold bound states' are stable is omitted, disappointing the more mathematically sophisticated reader. As the authors remark, the proof involves a special type of index theory involving non-Fredholm operators, and where one must deal with a continuous spectrum. The usual index theory breaks down since one is only dealing with elliptic operators, and contributions to the index from bosons and fermions do not necessarily have to be integers.
7. The authors should have included more discussion on mirror symmetry, beautiful subject that it is.
8. Dp-branes are asserted to be useful in incorporating non-Abelian gauge symmetries in string theory, in that they appear "naturally" as confined to world volumes of multiply-coincident Dp-branes. But is this the best way to introduce these symmetries? Is there a method, other than this one and `compactification', that is just as "natural" and does not have the contrived element that the introduction of Dp-branes sometimes has?
9. The authors need to elaborate in more detail on the definition of "stable" and "unstable" D-brane.
10. The omitting of the proof that string theories are ultraviolet finite theories of quantum gravity. This is by far the most serious omission in the book. This reviewer does not know of a reference that proves this assertion, and many in the physics community have pointed to this omission as being a sign that the string theory research community has been misled by false assertions of proof.