Physics 234A: String Theory I

Fall 2008

shortcut to the homework assignments
shortcut to the week-by-week outline

Basic Info

Instructor: Petr Hořava (email: horava@berkeley.edu)
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. Last year's 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 correspondence.

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 cancellation mechanism.
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 viewed here (for 234A: String Theory I), and here (for 234B: String Theory II).

Just as last year, a (rough) 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 schedule, see here.)

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).

horava@berkeley.edu