Physics 234A: String Theory I

Fall 2015

shortcut to the homework assignments

Basic Info

Time and place: Mon and Fri, 1:10pm - 2:30pm, 402 Le Conte (lectures);
Mon, 2:30pm - 3:30pm, 325 Le Conte (discussions)

Instructor: Petr Hořava (email:
Office: 401 Le Conte Hall.
GSI: Mudassir Moosa (email:

This course will give a thorough introduction to modern string theory.

In the past two decades or so, string theory has become the dominant theoretical framework for addressing questions about the fundamental structure of matter in our Universe. It has produced many new ideas and insights in other fields of physics, ranging from particle phenomenology to quantum gravity, cosmology, and more recently even to condensed matter systems. Some of this surprising power of string theory is logically explained by the fact that string theory represents a natural extension or completion of the language of quantum many-body systems and quantum field theory, which makes it relevant in all those diverse areas where the methods of many-body physics play an important role. Basics of string theory should now be in every theorist's vocabulary, regardless of the specific field of physics.

Our main goal in this semester will be two-fold. On one hand, we will develop some practical understanding of the basic elements and techniques of string theory. On the other hand, we will also focus on understanding the "big picture" -- how string theory produces new ideas and techniques relevant to other areas of physics besides particle phenomenology and quantum gravity. In that part of the semester, we will particularly discuss some recent interactions of string theory with condensed matter (via the AdS/CFT duality, but also stimulating the development of topological insulators), and with inflationary cosmology (which we will frame in the language of the effective field theory of inflation).

Throughout the semester, I will also point out some of the open questions and puzzles of our field. String theory is a live and rapidly developing field, which promises that many interesting surprises are still to come, especially in the cross-disciplinary areas of condensed matter, cosmology, and perhaps others (AMO physics? Nonequilibrium systems? Quantum computing?). Anticipating such future developments is one of the most exciting challenges in string theory today.

Specifically, in this semester we will cover the following six areas:

I. Introduction: Why strings?
II. The bosonic string.
III. Superstrings, heterotic strings, supergravity.
IV. D-branes.
V. M-theory and string dualities.
VI. Applications in condensed matter & inflationary cosmology.
(UPDATE: Since as it turns out I will also be teaching 234B: String Theory II in Spring 2016, I have decided to postpone Part VI until the Spring, when we will have a better chance to cover these advanced topics in more detail. Fall 2015 will thus focus on Parts I-V listed above.)

The style will be somewhat similar to the style of my course taught in Fall 2008, Fall 2009, and Fall 2011. However, as the field is evolving, we will take a novel, fresh look at some of the basic questions and applications of string theory in the context relevant for current research. The main textbook is going to be

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

we will occasionally use other resources, including the two volumes of Joe Polchinski's book, the classic two volumes of Green-Schwarz-Witten, or the newer book by Elias Kiritsis (String Theory in a Nutshell), and sometimes even review papers from the arXiv. We will also take a closer look at the new exciting book

D. Baumann and L. McAllister, Inflation and String Theory (Cambridge University Press, 2015),

just published by CUP in April.


In order to make Physics 234A accessible to a wide audience of students from varying areas of physics and cosmology, I will develop the material from first principles, such that the course can be taken without any prior knowledge of quantum field theory (for example, it could be taken concurrently with -- or even before -- 232A). Some basic understanding of quantum mechanics and relativity is however assumed.

Grading Policy

The final grade will be based on three things: 1. homeworks, 2. participation in discussions (during discussion sessions as well as lectures), and 3. the final exam. As I have done with other classes in previous years, I will again apply the "two-out-of-three" rule, which was explained clearly in class. Briefly, it means that for a good grade (say an A) it is sufficient to do really well on two out of 1., 2. and 3. listed above; for example, if you do great on homeworks and you interact well in discussion sessions and lectures, you will be exempt from the final exam. (Other permutations work as well.) Update (December 7): I am very pleased to announce that this year, all students who stayed registered for the course received an A or an A+ grade (or a PASS if they signed up on the pass/fail basis), and no-one will be asked to do the final exam. Thank you for your hard work, and congratulations to all for the job well done!

Homework Assignments

Homework assignments will be posted on this website weekly (or sometimes biweekly), likely on Mondays before 5pm. The assignments will be due in one week's time, on Monday, in class.

Most homeworks will be assigned from the list of Homework problems in Becker&Becker&Schwarz ([BBS]), unless stated explicitly otherwise. Occasionally, the assignment will contain also solved Exercises from [BBS]; if so, the students are encouraged to solve the problem before they look at the solution in [BBS].

HW 1 (posted on Aug 31): This week, we have a reading assignment, with nothing to be turned in. The assignment consists of two parts:
J.H. Schwarz, The Early History of String Theory and Supersymmetry, arXiv:1201.0981.
Chapter 1.1 of M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory, Vol. 1.

HW 2 (posted on Sept 7; due on Monday, Sept 14, in class): Problems 3.1, 3.2 and 3.3 (on page 106) from [Becker,Becker,Schwarz] (=[BBS]).

HW 3 (due on Monday, Sept 21, in class): Problem (1): Show that the Nambu-Goto action for the bosonic string (as given in Eqn. (2.11) on p. 24 of [BBS]) is invariant under worldsheet diffeomorphism transformations.
Problem (2): Take the nonrelativistic limit of the Nambu-Goto action, and solve Exercise 2.7 (on p. 27 of [BBS]) without looking at the solution provided there.
Problem (3): Using any triangulation(s) of your choice, calculate the Euler number of the torus.
Problem (4): Determine (the lowest value of) the genus of the compact two-dimensional surface on which you can draw the following Feynman diagram of a large-N theory of matrix degrees of freedom:

HW 4 (due on Monday, Sept 28, in class): Problems 2.3(i), 2.5, 2.9 and 2.13 of [BBS] (on pp. 54-57).

HW 5 (due on Monday, Oct 5, in class): Problems 3.4, 3.5, 3.6, 3.7 and 3.10 of [BBS] (pp. 106-7).

HW 6 (due on Monday, Oct 12, in class): Problems 3.11, 3.12, and 3.14 of [BBS] (pp. 107-8).

HW 7 (due on Monday, Oct 19, in class): Problems 4.4, 4.6, 4.7 and 4.11 [BBS] (pp. 145-6).

HW 8 (due on Monday, Oct 26, in class): Problems 5.1, 5.7 and 5.8 of [BBS] (pp. 184-6).

HW 9 (due on Monday, Nov 2, in class): In a slight change of pace, this week's homework offers one Problem and a bunch of solved Exercises from [BBS]. Please try to solve the Exercises before reading the solutions!
Exercises 7.3 (page 280), 7.6 (p. 283), 7.8 (p. 284), and Problem 7.1 (page 291).

HW 10 (due on Monday, Nov 9, in class): Problems 7.8, 7.10 (p. 293), 6.2, 6.3 and 6.4 (p. 245).

HW 11 (due on Monday, Nov 16, in class): Exercises 6.4 (p. 215) and 8.2 (p. 299), Problems 8.3 (p. 351) and 8.5 (p. 352).

HW 12 (this is our last HW assignment of the semester, due IN TWO WEEKS, on Monday, Nov 30, in class): Problems 5.9, 5.11 and 5.13 (p. 186), Problem 8.10 (p. 352), and Problem 12.1 (p. 686).