Gauge/Gravity Duality: Foundations and Applications

Any methodology for solving difficult problems in string theory or quantum field theory that seems to show some promise is always welcomed by practitioners in these two areas. Historically, most of the emphasis has been in perturbative calculations, which cannot be used for problems that involved strong coupling, such as quantum chromodynamics or the general bound state problem in quantum field theory. This book outlines an interesting approach to these types of problems that is based on a paper that was written by Juan Malcadena in 1998 and which has instigated a considerable amount of research since then. Marketed (with some justification) as a technique for studying strongly coupled field theories, the AdS/CFT correspondence is described as a map relating gravitational theories on asymptotically Anti-de Sitter spacetimes to conformal field theories. Those readers who want to familiarize themselves with this approach, and the more general methodology that is designated as ‘gauge/gravity duality’, will find the presentation adequate, as long as they are very familiar with superstring theory, supergravity, the mathematical formalism of general relativity, quantum chromodynamics, and of course conformal field theories in their different guises. The authors do give and overview of some of this background in the first four chapters, but readers who are not familiar with this material may find it heavy-going and too terse. Some readers may be skeptical regarding the claim that N = 4 super Yang-Mills theory in 3 + 1 dimensions is “dynamically equivalent” to type IIB superstring theory on AdS(5) X S(5). The authors define this dynamical equivalence to mean that both theories describe the same physics from two different perspectives, but since experimental evidence is what determines the viability of physical theories, this claim seems extravagant at the present time. The reviewer prefers viewing this correspondence in terms of “tools of calculation” for performing difficult derivations in one side of the correspondence by mapping it to the other. In addition, some readers may be disappointed to learn that most of the calculations in the opening sections are done in the weak coupling limit on the string theory side. These readers, the reviewer being one of them, have expectations that the AdS/CFT correspondence is used to study non-perturbative phenomena, and therefore any talk about doing perturbation calculations is somewhat of a disappointment. The authors though are apparently aware of some of the current skepticism regarding the applicability of gauge/gravity duality and therefore spend a few chapters on how it can function as a calculation tool in areas such as quantum chromodynamics (QCD) and condensed matter. In fact, two entire chapters are spent on QCD, with emphasis on how gauge/gravity duality can be applied to the confinement problem and to chiral symmetry breaking, in spite of the fact that QCD has no underlying supersymmetry. After studying these chapters, readers who need a more in-depth treatment will be prepared to consult the references or more advanced works on the subject.

I love this book is a hard reading but nonetheless very very interesting. It has a total of 15 chapters divided in three main parts I have only gone through PART I (Prerequisites): 1-Elements of field theory; 2-Elements of Gravity; 3-Symmetries in Quantum field theories; 4 -Introduction to superstring theory. I must say that these chapters are excellent they are not easy but they are worth the reading you must know already all of these if you want to get into the AdS/CFT correspondence anyway. Then I have gone only through the first chapter of the second part, PART II (Gauge/Gravity Duality) : 5-The AdS/CFT correspondence, apart from this chapter it brings this second part also the chapters 6-Tests of the AdS/CFT correspondence; 7- Integrability and Scattering amplitudes; 8-Further examples of the AdS/CFT correspondence; 9-Holographic renormalization group flows; 10-Duality with D-Branes in Supergravity; 11-Finite Temperature and density. Also brings a PART III (Applications) with four more chapters, this book is AMAZING! for an amazing topic the AdS/CFT correspondence of Juan Maldacena discovered back in 1998!

Useful reference text for specialists and postgraduates entering the field.

A very nice book, with a good selection of topics in this huge field of physics, and useful reviews of basic previous results needed for understanding the core theme of the book. Useful.

Hace una descripcion detallada del gauge en la gravedad cuantica y sobre todo de la importancia del gauge en la descripción de la gravedad

excellent book !!

I was recommended this book as an introduction to AdS/CFT correspondence, and pretty much everything about it has disappointed me. I'll start with the less important stuff, the physical side. When the book arrived, I was very surprised to find it take up a lot of space. It's only 2-3cm thick but the face of the book is the largest I own. Typically, more advanced physics textbooks opt for thickness over area, so this book is immediately striking as a first year textbook. Of course this isn't a huge deal, but some may be turned off by it. It's pretty eye catching due to its size so it's a bit awkward to read in public, and they layout makes me feel like I'm reading a book for a first year course, which is just generally a layout I don't particularly enjoy. The size also makes it a bit of a nuisance to carry around. Next, the actual quality of the book is pretty bad. I'm very careful with my books (text or otherwise) as I prefer to keep them in as pristine a condition as possible, and despite this, the spite became detached from the hard cover after 2 days of light use. Even people who treat their books with a lower amount of care should expect a book to last longer than 2 days. On to the more important stuff, the actual content of this book. Going over the review sections for QFT and GR was interesting as it addressed a couple things in ways I hadn't considered them before, and I thought that was nice, but oh dear do they cover those topics fast. That's fine though, as anyone interested in gauge/gravity duality should have a solid base in both. But that's where it ends. After those topics, everything else is still written like a review. It's written at too low a level for anyone who already knows about the topics discussed, but far too high a level to act as an introduction to any of the topics. A particular example is when they explicitly define tensors (like many other intro textbooks on things like differential geometry or GR) but then just assumes the reader knows tensor products. If the reader were so new to the material that they need tensors defined, they absolutely need tensor products defined, and if they're so advanced that they don't need the latter, they certainly don't need the former. The brief, unclear text also doesn't help the situation. Every section is a short mix of both intro and full review. Of course I expected a brief review of QFT and GR as those are huge topics which should be considered prerequisite material, but I was understandably confused when they offered the same treatment for both AdS space and conformal symmetry. For a book whose focus is AdS/CFT, one would expect a more thorough introduction to both AdS and CFT. The problems listed in the book also seem tangential to the actual material; some of the earlier problems in QFT and GR were trivial, as a reader with a background in both, but once it starts getting to new material it seems the reader needs a much deeper background outside of what's offered in the text. Perhaps I'm mistaken here but that was my impression. At the end of the day, I've learned very little from this cumbersome book and recommend quite strongly against it.