Physics 234B: String Theory II
shortcut to the
list of reading assignments
shortcut to the references and additional reading
Time: lectures: Tue and Thu, 12:40-2pm;
discussions will start later in the semester (likely on March 14),
and they will alternate (in a manner to be posted on this webpage) between
Thu 2:10-3pm and 4:10-5pm.
Place: 402 Le Conte Hall
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
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
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.,
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
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.
Additional Reading Materials
Week 1: Introduction and overview of dualities; outline of the course.
No specific references, besides the recommended texts mentioned above.
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
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
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
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
An Unorthodox Introduction to Supersymmetric Gauge Theory,
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
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:
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,
String Theory in Two Dimensions, arXiv:hep-th/9106019,
Liouville Field Theory: A Decade after the Revolution,
And finally, three papers about an extension of matrix models to
P. Hořava and C.A. Keeler,
Noncritical M-Theory in 2+1 Dimensions as a Nonrelativistic Fermi
Noncritical M-Theory and the Topological A-Model
Strings on AdS(2) and the High-Energy Limit of Noncritical M-Theory,
Homeworks, Reading Assignments and Grading
There will be no formal homework assignments in this course. Instead, there
is a list of reading
consisting of a number of exciting or otherwise fundamentally important recent
papers which would be tangential to the main line of reasoning in the
lectures, but which will enrich our understanding of the big picture and of
future applications of AdS/CFT and other dualities. Each student will sign
up for one paper from the list, will study it, type a two-page executive
summary, and present the logic and results of the paper to the class in a
discussion session. These student presentations will be scheduled for the
second half of the semester, at the rate of two presentations per
session (i.e., each student gets 20 minutes plus 5 minutes of discussion).
(The presentations will commence from the first Thursday in April, i.e.,
the first Thu after Spring break.)
Having completed such a presentation, the student will have satisfied the
requirements for an A (together with the attendance of lectures themselves).
For such students, there will be no final exam.