Physics 234B -- String Theory II:

Beyond the Alphabet

Spring 2016

shortcut to Miscellaneous References

Basic Info

Lectures: Tue and Thu, 12:40-2pm, 402 Le Conte Hall.
Discussions: will start later in the semester, and will contain students' presentations of their selected reading assignments.
Time and place: Thursdays 4:10-5pm, Fridays 1:10-2pm, 402 Le Conte. We will alternate between the two time slots, the exact schedule of the discussion sessions will be posted just before Spring break.

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

Having learned the basic ingredients of the "string-theory alphabet" in an introductory course String Theory I, our focus in the second semester will be on exciting advanced topics in string theory, in which the various ingredients come together (and where intriguing open challenges remain). After polling the students in my Fall 2015 234A class, I have decided that we shall focus on four major themes, divided into four relatively equally important parts:

Part I. Holography: AdS/CFT Correspondence and Other Holographic Dualities.

Part II. String Geometry: Topological Strings, Compactifications, Elements of Mirror Symmetry.

Part III. Cosmological Inflation: From the Effective Field Theory Approach, to String Inflation.

Part IV. Open challenges of quantum gravity: Strings and Gravity out of Equilibrium; Keldysh-Schwinger Formalism, ... (additional possible topics in Part IV will be determined interactively based on the interests of the students in the class).

Some interesting textbooks that we may use (to varying degree) are:

K. Becker, M. Becker and J.H. Schwarz, String Theory and M-Theory. A Modern Introduction (Cambridge University Press, 2006).
[We used this book for our String Theory I last semester, and it will be our go-to for the basic ingredients of the theory.]

E. Kiritsis, String Theory in a Nutshell (Princeton University Press, 2007).
[Another good one-volume survey of the modern aspects of string theory.]

M. Ammon and J. Erdmenger, Gauge/Gravity Duality. Foundations and Applications (Cambridge University Press, 2015).
[A recent survey of the basics of AdS/CFT correspondence, a good reference text for AdS/CFT basics.]

D. Baumann and L. McAllister, Inflation and String Theory (Cambridge University Press, 2015).
[This will be our go-to text for our critical survey of inflation.]

J. Zaanen, Y.-W. Sun, Y. Liu and K. Schalm, Holographic Duality in Condensed Matter Physics (Cambridge University Press, 2015).
[I am very excited about this book, although I haven't seen much of it yet -- it could be brilliant! Certainly a good source for the first few weeks of the semester.]

Grading, Homeworks, Reading Assignments

There will be no homework sets for this course (only recommended reading materials, for those interested in something extra beyond the lectures). Instead of homeworks, there will be a list of reading assignments, which I will post early in the semester. Each student will choose one from a list of important or otherwise interesting string-related research papers. During the second half of the semester, the students will present their summary of the ideas and results of their chosen paper during our Discussion Sessions. The final grade will be based on this presentation. There will be no final exam.

Miscellaneous References & Reading Suggestions

Here I intend to post various comments, references and extra reading material options, on a weekly basis as we go through the material.

Week 1. A very interesting review of the basics of perturbative string theory is the first half of Joe Polchinski's 1994 TASI lectures:
J. Polchinski, What is String Theory?, arXiv:hep-th/9411028.
This paper is particularly interesting, as it was written just before the "2nd Superstring Revolution" (which happened in 1995), and there are probably useful lessons to learn from this paper in this day as well.
Reference [1] of Polchinski's TASI lectures is Ken Wilson's 1982 Nobel lecture, which should also be a mandatory reading for everyone who wishes to study QFT or many-body physics (and, by extension, string theory) -- it represents a fascinating brief account of, and introduction into, the Wilsonian renormalization group paradigm, the most important conceptual platform for almost everything we will do this semester:
K.G. Wilson, The Renormalization Group and Critical Phenomena, Rev. Mod. Phys. 55 (1983) 583.
And finally (at least for the references to our first lecture), a brief early history of string theory can be found in
J.H. Schwarz, The Early History of String Theory and Supersymmetry, arXiv:1201.0981.
The large-N expansion: The elegant large-N solution of QCD in two dimensions using light-cone gauge is in the short paper (only ten pages long!):
G. 't Hooft, A Two-Dimensional Model for Mesons, Nucl. Phys. B75 (1974) 461.

Week 2. G. 't Hooft's 2002 review of large N is here:
G. 't Hooft, Large N, arXiv:hep-th/0204069.
A nice "classic" review of the large N limit as a classical limit is in:
L.G. Yaffe, Large N Limits as Classical Mechanics, Rev. Mod. Phys. 54 (1982) 407.
As mentioned in class, with a few relatively uninteresting exceptions, scale invariance in a relativistic QFT implies full conformal invariance, but the precise statement is still work in progress. For an interesting recent contribution to this subject, with references to relevant older papers, see for example:
A. Dymarsky and A. Zhiboedov, Scale-Invariant Breaking of Conformal Symmetry, arXiv:1505.01152.

Week 3. The proof that N=4 super Yang-Mills is UV finite, and hence a CFT, was given by our very own Stanley Mandelstam :) in:
S. Mandelstam, Light-cone Superspace and the Ultraviolet Finiteness of the N=4 Model, Nucl. Phys. B213 (1983) 149.
The method he used? You guessed it ("whenever in doubt about a new, complicated theory ...") -- he used a light-cone version of superspace! Well, it also says that in the title ...
The groundbreaking paper that gave rise to the entire field of AdS/CFT correspondence is of course
J.M. Maldacena, The Large N Limit of Superconformal Field Theories and Supergravity, arXiv:hep-th/9711200.
So far, this paper has over 11,000 citations, and counting.
The two groundbreaking papers which presented the idea of gravitational holography are:
G. 't Hooft, Dimensional Reduction in Quantum Gravity, arXiv:gr-qc/9310026,
L. Susskind, The World as a Hologram, arXiv:hep-th/9409089.

Week 4. The lecture on Tuesday, February 9 will be given by a guest speaker, Stefan Leichenauer. He will talk about the recent results on the quantum version of the null energy condition, from the perspective of holography and large N.

Prerequisites

Basics of General Relativity at the level of 231 and of QFT at the level of 232A would be great. Some basic knowledge of the "string alphabet", rougly at the level of my String Theory I course, are required, but having completed the official 234A course is not strictly a prerequisite -- I encourage all students interested in the material to sign up for this course, regardless of prior background. If you are interested in this course and have questions about having all the prerequisites, feel free to talk to me (in person or via email); I will try to be flexible, my intention is to accommodate as many students in this course as possible, even those who come from various diverse backgrounds such as particle phenomenology, cosmology, condensed matter, or pure math.

horava@berkeley.edu