Physics 234A: String Theory I

Fall 2009

shortcut to the homework assignments

Basic Info

Time: Tue and Thu, 11:10am-12:30pm (lectures); Thu 2:10-3:00pm (discussion sessions)
Place: 402 Le Conte Hall

Instructor: Petr Hořava (email:
Offices - campus: 401 Le Conte Hall; LBNL: 50A-5107.

The course will focus on the introduction to modern string theory. In the Fall semester, we will cover the following five areas:
I. Introduction: Why strings?
II. Superstrings and supergravity.
III. D-branes.
IV. Black holes and branes; stringy answers to puzzles of quantum gravity.
V. Nonperturbative string-string dualities and M-theory; selected advanced topics.
The style will be similar to the style of last year's course. This course 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 new book by Elias Kiritsis (String Theory in a Nutshell), and sometimes even review papers from the arXiv.

Homework Assignments

Homework assignments will posted on this website on Thursdays. The assignments will be due either in one week or in two weeks after their posting, on Thursday in class. Solutions of the homework problems will then be discussed in the Discussion Session, scheduled for Thursdays 2:10-3pm in 402 Le Conte.

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 Thu, Sept 10): The first three problems are solved exercises from [BBS]: Exercise 2.2, 2.3 and 2.6 (on pages 21 and 26 of [BBS]). The fourth problem is not from [BBS]: In class, 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, derive Stirling's formula by approximating the integral expression for the Euler gamma function by a Gaussian.

HW2 (due Thu, Sept 24): Problems 2.5, 2.6, 2.13, 2.14 and 2.4 (pages 55-57 of [BBS]).

HW3 (due Thu, Oct 1): Problems 2.11 and 2.12 (on page 57); in addition, prove that the Faddeev-Popov determinant as introduced in class is gauge invariant.

HW4 (due Thu, Oct 8): Problems 3.14 and 3.15 (on page 108 of [BBS]); in addition, show that the BRST charge squares to zero, by showing that the BRST transformations on all fields (for the generic gauge theory as discussed in class) square to zero. (This is of course trivial for the antighost and the auxiliary field, the interesting part is to prove the same for the matter fields and the ghosts.)

HW5 (due Thu, Oct 15): Problems 3.4, 3.7, 3.10 and 3.11 (on pp. 106-7).

HW6 (due Thu, Oct 29): Problems 4.2, 4.4, 4.6, 4.7 and 4.11 (pages 144-6 of [BBS]).

HW7 (due Thu, Nov 12): Problems 5.7, 5.8, 5.9 (i) and (ii), 5.11 and 5.13 (pages 185-6 of [BBS]).

HW8 (due Thu, Nov 19): Problems 6.1, 6.3 and 6.4 (pages 244-5 of [BBS]).

HW9 (due Thu, Dec 3): Problems 6.5 (beware of typos in Eqn. (6.94)!), 6.7(i), 6.12, 8.3, 8.7 and 8.8.