Physics 234A: String Theory I

Fall 2011

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Basic Info

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

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 played a powerful role as a generator of 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. It has also played a revolutionary role in many recent developments in mathematics. Some of this surprising power of string theory is perhaps 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.

The main aim of this course is to develop a practical understanding of the basic elements and techniques of string theory, touching on many of the long list of conceptual successes and insights it offers. We will also discuss some of the open questions and puzzles, stressing that string theory is a live and rapidly developing field, which promises many interesting surprises still to come in the future. Anticipating such future developments is one of the most exciting challenges in string theory today.

In the Fall semester, we will cover the following six areas:

I. Introduction: Why strings?
II. The bosonic string.
III. Superstrings and supergravity.
IV. D-branes.
V. The heterotic string.
VI. Nonperturbative string-string dualities and M-theory; selected advanced topics.

The style will be similar to the style of the course taught in Fall 2008 and Fall 2009. Physics 234A represents a detailed introduction to string theory, and can be taken without any prior knowledge of quantum field theory (for example, it could be taken concurrently with 232A).

The main textbook is again 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.

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].

HW1 (due Fri, Sept 9, in discussion session): This warm-up homework assignment contains just one problem: In our first discussion session, we used Stirling's formula which approximates the Euler gamma function at the large positive values of its argument. As a simple exercise in Gaussian integrals (which play a prominent role in quantum field theory), derive Stirling's formula by approximating the integral expression for the Euler gamma function by a Gaussian. [Useful references: Chapter 1.1 of Volume 1 of Green-Schwarz-Witten for the role of Stirling's formula in estimating the high-energy behavior of the Veneziano amplitude; A. Zee's book Quantum Field Theory in a Nutshell for an introduction to Gaussian integrals in quantum field theory.]

HW2 (due Fri, Sept 16, in discussion session): [All problems of this assignment are solved Exercises from [BBS]; please solve them first, before consulting the official solutions in the book.]
Exercises 2.2 and 2.3 (page 21 of [BBS]), Exercise 2.4 (page 22), Exercise 2.6 (page 26).

HW3 (due MONDAY, Sept 26, in discussion session at 11:10am): Problems 2.1, 2.4, 2.5, 2.9 and 2.13 (pages 53-57 of [BBS]).

HW4 (due Fri Oct 7): Problems 3.6, 3.7, 3.10 and 3.11 (on pages 106-107).

HW5 (due Fri Oct 21): Problems 3.12 and 3.14 (pages 107-8), Problems 4.4 and 4.7 (pages 145-6). In addition, show that the Faddeev-Popov determinant that we encountered in the path integral quantization of the bosonic string is gauge invariant (hint: [Polchinski]).

HW6 (due on Fri Nov 4): Problems 4.14 and 4.15 (page 147), Problem 5.8 (p. 185), Problems 6.1 and 6.2 (pp. 244-5).

HW7 (due on Fri Nov 18): Problem 6.2 left over from HW6, plus Problems 6.3, 6.7 and 6.12 (pp. 245-7).

HW8 (due on Fri Dec 2): Problems 7.3, 7.4, 7.8 and 7.14 (pp. 292-5); derive Eqn. (8.69) on page 317; and Problem 8.7 (p. 352). [NOTE: There was a typo in an earlier assignment of this HW8; the incorrect 7.17 should have been 7.14 (thanks, Eugene, for catching this!)]

horava@berkeley.edu