Physics 234B: String Theory II

Spring 2013

shortcut to the list of reading assignments
shortcut to the references and additional reading materials

Basic Info

Instructor: Petr Hořava (email: horava@berkeley.edu)
Office: 401 Le Conte Hall.

How can we teach a String Theory II if there was no prior 234A String Theory I course offered in Fall 2012? Simple! This will be a one-semester, advanced course focusing on AdS/CFT correspondence and other dualities, without any prerequisite knowledge of string theory. AdS/CFT is a powerful new technology, which originated from strings and M-theory, but which has a much wider impact -- ranging from high-energy theory and particle phenomenology, all the way to non-relativistic many-body theory and condensed matter physics. The goal of this semester is to give a good working knowledge of the basic principles and techniques of AdS/CFT correspondence, and to place it in the wider context of historical developments in dualities, as well as the open questions for the future applications.

There is no official required textbook, and we will mostly follow review articles from the arXiv and elsewhere. References and links to the relevant reading materials will be posted on this webpage on Thursdays afternoon.

If you still prefer having a reference textbook on string theory, there are two recommended textbooks for this course:

E. Kiritsis, String Theory in a Nutshell (Princeton U.P., 2007)

and

K. Becker, M. Becker and J.H. Schwarz, String Theory and M-Theory. A Modern Introduction (Cambridge U.P., 2006).

Prerequisites for this course are: One semester of Quantum Field Theory (at the level taught by me in Fall 2012, using mostly Peskin-Schroeder as the textbook), and some basic knowledge of concepts of General Relativity (a useful text to catch up on GR is S. Carroll's Introduction to Spacetime and Geometry). No string theory background is required, we will develop AdS/CFT and other dualities without strings (at least at first).

The outline of the course is going to be, roughly, as follows:

Our focus will be on gauge-gravity duality, of which AdS/CFT correspondence is the central example. We will motivate this duality from the large-N expansion in quantum field theory and many-body physics. Then we will retrace the history of some of the most important dualities, to prepare the ground for a detailed study of gauge-gravity dualities. We will start with dualities in the lattice models (including the Kramers-Wannier duality of the Ising model), then move on to dualities in QFT in two spacetime dimensions, including bosonization and sine-Gordon/Thirring duality. Throughout the semester, the emphasis will be on universality of dualities, stressing the fact that they exist not only in relativistic but also in non-relativistic systems. We will study 2D CFTs (partially because they are important for string theory), their supersymmetric cousins, and their twisted topological versions (relevant for dualities such as mirror symmetry). We will go back to the historical origins of string theory itself, in the form of so-called "dual models" of strong interactions, and rederive some basic features of string theory from scratch. We will discuss "old matrix models," as a powerful example of a triality relating matrix quantum systems, relativistic gravity and strings, and non-relativistic Fermi liquids. We will briefly touch on dualities in supersymmetric QFT in 3 and 4 dimensions.

Having gone through this background material, the rest of the semester (after the Spring break) will be devoted to AdS/CFT proper. We will develop concepts of holography in quantum gravity, the structure of basic supergravity theories, look at the black hole solutions and the role they play in describing the thermal behavior of dual QFTs. We will study not only relativistic AdS/CFT, but also its non-relativistic counterparts (rapidly developing in recent years). This will bring us in contact with modern theories of gravity with anisotropic scaling (a.k.a. Hořava-Lifshitz gravity :) and the structure of its holographic renormalization. Throughout the semester, we will touch on many exciting open research directions and applications of AdS/CFT and dualities in general.

Week 2: The idea of deriving basic AdS/CFT correspondence from the large N limit (and its relation to string theory) is beautifully reviewed in Maldacena's 2003 TASI Lectures on AdS/CFT, which I have followed in the lectures this week. The additional example of the Gross-Neveu model at large N is discussed in Chapter VII.4 of A. Zee's Quantum Field Theory in a Nutshell. (As in my 232A in Fall 2012, all my references to Zee are to the second edition of the book, which I strongly recommend over the first edition.) Chapter VII.4 of Zee also contains lots of fascinating aspects of the large N story which we probably won't be able to go into too much in lectures.

Week 3: We continued with the basics of AdS/CFT. Then, we have started the chapter on dualities in the lattice model, focusing first on the Ising model Kramers-Wannier duality. A great reference for dualities in lattice models is the review paper by R. Savit, Duality in Field Theory and Statistical Systems, Rev. Mod. Phys. 52 (1980) 453. This paper was published in 1980, which shows how mature the subject of dualities in statistical mechanical system really is. It is still a lot of fun to read that review today!

Week 4: After seeing the Savit review, a really nice follow-up reading is another review, by J. Kogut, An Introduction to Lattice Gauge Theory and Spin Systems, Rev. Mod. Phys. 51 (1979) 659, as well as his slightly more recent review J. Kogut, The Lattice Gauge Theory Approach to Quantum Chromodynamics, Rev. Mod. Phys. 55 (1983) 775. Both of these papers are a beautiful summary of the basic ideas, concepts and dreams of the original wave of research in lattice gauge theories, much of which still remain very relevant today. In addition, there is a very good quick summary of lattice Yang-Mills in Chapter VII.1 of Zee (after his introduction to Yang-Mills in Chapter IV.5).

Week 5: This week was focused on hydrodynamic aspects of AdS/CFT, with Omid Saremi as our guest lecturer. A great review, covering this topic at just the right level, is D.T. Son and A.O. Starinets, Viscosity, Black Holes, and Quantum Field Theory, arXiv:0704.0240, which I recommend as the additional reading material for this week.

Week 6: The duality between compact U(1) gauge theory and the XY model in 2+1 dimensions is described for example in X.-G. Wen's book Quantum Field Theory of Many-Body Systems (Oxford U.P., 2004), in Chapter 6.3 (this was the source that we mostly followed in the lectures), or in A.M. Polyakov's book Gauge Fields and Strings, see especially Chapter 4. This book may be older, but it contains lots of great and often subtle insights into the structure of quantum field theory and string theory. Certainly worth reading!

Weeks 7 and 8: We discussed mostly CFTs in two dimensions, both as a part of the perturbative definition of what string theory is, and also on their own. Some useful references are: is P. Ginsparg, Applied Conformal Field Theory, arXiv:hep-th/9108028, which reviews the basics, including bosonization; the big encyclopedia by P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory (Graduate Texts in Contemporary Physics, Springer, 1996); a particularly nice review of supersymmetric CFTs with mathematical applications to mirror symmetry, string theory etc are B.R. Greene, String Theory on Calabi-Yau Manifolds, arXiv:hep-th/9702155. The microscopic derivation of black-hole entropy in terms of counting asymptotic states in dual CFT using the duality between gravity in AdS space in 2+1 dimensions and two-dimensional CFT was following the paper by A. Strominger, Black-Hole Entropy from Near-Horizon Microstates, arXiv:hep-th/9712251, (written only a month after the original AdS/CFT paper by Maldacena!).

Week 9: In this week, the guest lecturer Ori Ganor will discuss various aspects of dualities in supersymmetric gauge theories in 3+1 dimensions, and their origin from 5+1 dimensions. This is a vast subject, with many twists, turns and ramifications (especially once we start reducing the number of supersymmetries away from maximal SUSY) -- one of my favorite "big-picture" reviews on supersymmetric gauge theories and some of the relevant phenomena that is definitely worth reading is M. Strassler, An Unorthodox Introduction to Supersymmetric Gauge Theory, arXiv:hep-th/0309149.

Week 10: Spring break: No lectures this week, but if you are looking for suitable reading material and have not read the review by Strassler cited above, read that one!

After Spring break: The weeks after Spring break are devoted to the students' presentations of their reading assignments in the discussion sessions.
Here is the pdf file of my trasparencies on Lifshitz Gravity for Lifshitz Holography, as used in class and requested by the students.
In one of the presentations, the issue of light-front formulation of string theory/M-theory came up. There is a beautiful review paper of these issues, especially in relation to M(atrix) theory: J. Polchinski, M Theory and the Light Cone, arXiv:hep-th/9903165.
As stressed in lectures, many modern features of quantum gravity, string theory, holography, AdS/CFT, closed-open string duality etc etc had been hiding in the old matrix model approach to string theory. Here are three excellent review papers on old matrix models (including one with the modern take on them):
P. Ginsparg and G. Moore, Lectures on 2D Gravity and 2D String Theory, arXiv:hep-th/9304011,
I.R. Klebanov, String Theory in Two Dimensions, arXiv:hep-th/9106019,
Y. Nakayama, Liouville Field Theory: A Decade after the Revolution, arXiv:hep-th/0402009.
And finally, three papers about an extension of matrix models to noncritical M-theory:
P. Hořava and C.A. Keeler, Noncritical M-Theory in 2+1 Dimensions as a Nonrelativistic Fermi Liquid, arXiv:hep-th/0508024, Thermodynamics of Noncritical M-Theory and the Topological A-Model ,arXiv:hep-th/0512325, Strings on AdS(2) and the High-Energy Limit of Noncritical M-Theory, arXiv:0704.2230.

horava@berkeley.edu