Physics 234A: String Theory I
shortcut to the homework assignments
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Time: Tue and Thu, 11:10am-12:30pm (lectures);
Fri 3:10-4pm (discussion sessions)
Place: 402 Le Conte Hall
Offices - campus: 401 Le Conte Hall; LBNL: 50A-5107.
Over its forty years of existence, string theory has developed into one
of the dominant paradigms in modern theoretical physics. String theory is
not only a leading candidate for the quantum theory of gravity, but it has
also been remarkably successful as a theretical framework capable of
influencing other fields of physics and mathematics: In particular, string
theory has led to surprising new ideas, techniques and insights in areas
ranging from particle phenomenology and cosmology, to condensed matter
theory, to differential geometry and algebraic topology. As a result,
understanding the basic concepts and tools of string theory has become
invaluable for any theoretical physicist.
This is the second year in a row that String Theory at Berkeley will be
taught as a regular one-year course, under the 234A/B sequence.
String Theory I (and
String Theory II)
was a success, and a lot of fun. This semester, 234A will follow a very
similar pattern as last year, with the main textbook again being
K. Becker, M. Becker and J.H. Schwarz, String Theory and M-Theory.
A Modern Introduction (Cambridge U.P., 2006);
we will make occasional detours into extra material, using either
J. Polchinski's String Theory books, the classic Green-Schwarz-Witten,
E. Kiritsis's new book, or variour review articles.
The focus of the first semester will be on the basic ideas and techniques,
mainly in string perturbation theory. Last year, this was followed in the
second semester by nonperturbative dualities, M-theory, and AdS/CFT
In more detail, the main themes of the Fall semester will be:
I. Introduction: why strings?
II. The bosonic string: worldsheet action, quantization (including
BRST), open and closed string spectra, string perturbation theory,
two-dimensional conformal field theory (CFT), scattering amplitudes,
spacetime effective action, ...
III. Superstrings: worldsheet supersymmetry and the NSR formalism,
superconformal field theory (SCFT); spacetime supersymmetry and the
Green-Schwarz formalism; spacetime effective supergravity.
IV. D-Branes: the perturbative worldsheet description of D-brane
solitons using open strings; the boundary-state description; basic properties
of D-branes, T-duality; orientifolds.
V. Heterotic strings: toroidal compactifications, lattices, bosonic
and fermionic formulation of heterotic strings; the Green-Schwarz anomaly
VI. Selected special topics: Elements of Calabi-Yau compactifications,
exact CFT's, emergence of spacetime physics; string dualities and AdS/CFT,
string theory out of equilibrium, etc. (the precise selection of topics
in Theme VI will depend on the students' interests)
The official department syllabus for these (still very new) courses can be
here (for 234A:
String Theory I), and
here (for 234B:
String Theory II).
Just as last year, a
week-by-week schedule is now posted. More details will be filled in as
the semester progresses; also, later adjustments and fine-tunings to the
outline are likely, at least partially in response to the interests of the
students enrolled in this class. (For last year's detailed week-by-week
There will be a total of six homework assignments, posted on this
website once every two weeks on Thursdays before 6pm. The assignments
will be due in two weeks after their posting, on Thursday in class.
Solutions of the homework problems will then be discussed in the Discussion
Session on Friday (3:10-4pm 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 25):
Exercise 2.2 (on page 21 of [BBS]),
Exercises 2.8 and 2.9 (on pp. 28-29 of [BBS]); Problems 2.5, 2.13 and 2.14
(on pp. 55 and 57).
HW2 (due Thu, Oct 9): Problems 2.12 (p. 57),
3.4, 3.7, 3.10, 3.11 and 3.14 (pp. 106-108). In addition, as a bonus
problem, you can prove that the Faddeev-Popov determinant discussed in
class is gauge invariant.
HW3 (due Tue, Oct 28): Problems 4.2 part (ii)
and (iii), 4.5, 4.7, 4.10 and 4.13 (pp. 144-146 of [BBS]).
HW4 (due Thu, Nov 6): Problems 5.5 and 5.8 (p. 185),
Problems 6.1, 6.5 and 6.9 (pp. 244-246).
HW5 (due Thu, Nov 20): Problem 6.15 (p. 248),
Problems 7.3, 7.5, and 7.8 (pp. 292-293).
HW6 (due Thu, Dec 4): Problems 5.9 (i) and (ii),
5.15 (page 186); Problems 8.7 and 8.8 (page 352).