Physics 234A: String Theory I
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Time: Mon and Fri, 1:10pm - 2:30pm (lectures);
Fri 11:10am - 12noon (discussion sessions);
please reserve also Mondays 11:10am - 12noon, some discussions will
be moved from Fri to Mon.
Place: 402 Le Conte Hall
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
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.
V. The heterotic string.
VI. Nonperturbative string-string dualities and M-theory; selected
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
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,
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
Homework assignments will posted on this website on Friday afternoons,
sometimes weekly sometimes biweekly.
The assignments will be due in the 11:10am discussion session (with the
precise date indicated as each assignment is posted), and we will
discuss the solutions in that same session.
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
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
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:
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!)]