Physics 234A: String Theory I

Fall 2007

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Basic Info

Instructor: Petr Hořava (email: horava@berkeley.edu)
Offices - campus: 401 Le Conte Hall; LBNL: 50A-5107.
GSI: Cindy Keeler (email: ckeeler@berkeley.edu)
Office - campus: 420K Le Conte Hall

This is the first time, in the history of Berkeley, that String Theory will be taught as a regular one-year course, under its newly approved official numbers 234A,B! The official syllabus for these new courses can be viewed here (for 234A: String Theory I), and here (for 234B: String Theory II).

The exact implementation of the course will always somewhat depend on the instructor. This year, the main official textbook will be

K. Becker, M. Becker and J.H. Schwarz, String Theory and M-Theory. A Modern Introduction (Cambridge U.P., 2006),

but we will make frequent detours into extra material, using either J. Polchinski's String Theory books, the classic Green-Schwarz-Witten, or variour review articles.

The focus of the first semester will be on the basic ideas and techniques of string perturbation theory; the second semester will delve into nonperturbative dualities, M-theory, and AdS/CFT correspondence. Thus, 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. Classical solutions of string theory: Elements of Calabi-Yau compactifications, exact CFT's, emergence of spacetime physics etc.

A tentative week-by-week schedule has been posted here; frequent adjustments of that schedule are likely.

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 13): Exercises 2.2 and 2.5 (page 21 of [BBS]), Problem 2.1 (page 53). In addition, there is one problem not from [BBS]: consider the spacetime propagator of a free scalar field in 1+1 dimensions as discussed in class, and introduce a small mass as the infrared regulator; calculate the leading term in the asymptotic expansion of the propagator in the powers of the infrared regulator (i.e., determine the precise coefficient in front of the log term in the expansion, and show that it is the only term diverging as the IR regulator is taken to zero).

HW2 (due Thu, Sept 20): Problems 2.13, 2.14, 2.15 (p. 57 of [BBS]).
In addition, two problems that are not in [BBS]:
(i) Check the Faddeev-Popov determinant as discussed in class (or in Ch. 3 of [Polchinski I]) is gauge invariant.
(ii) Check that the BRST transformation in a generic gauge theory (as defined in class, or in Formula (4.2.6) of [Polchinski I]) squares to zero, by applying two consecutive BRST transformations to all fields.

HW3 (due Thu, Sept 27): Problems 2.4(ii) and (iii) (on page 55), 3.7, 3.8, 3.11, and 3.14 (on pages 106-8) of [BBS].

HW4 (due Thu, Oct 4): Since there are no homework problems on tree-level string scattering amplitudes in [BBS], we have to resort to [Polchinski]. The following problems are on pages 204 and 205 of [Polchinski I]: 6.4(a) and (b), 6.5(a), and 6.8.

HW5 (due Thu, Oct 11): Problem 3.10 (page 107 of [BBS]). In addition, read Section 8.5 of [Polchinski I], and Section 15.1 of [Polchinski II]. The remaining two problems are from [Polchinski]: 15.1 and 15.2 (on page 271 of [Polchinski II]).

HW6 (due Thu, Oct 18): Problems 4.5, 4.7, 4.11 and 4.12 (pages 145-146 of [BBS]). In addition, Exercise 4.11 (on page 139 of [BBS]) is useful, if you try it first before looking at the answer.

HW7 (due Thu, Oct 25): Problems 4.14 and 4.15 (page 147), problems 5.1 and 5.3 (pages 184-185) of [BBS]. In addition, reading Chapter 10.4 of [Polchinski II], on the bosonization of the superghosts, might be useful.

HW8 (due Thu, Nov 1): Problems 5.7 and 5.8 (page 185), problems 7.3 and 7.5 (page 292) of [BBS]. (Hint: The nonsupersymmetric SO(16) x SO(16) heterotic string is discussed in Chapter 11.3 of [Polchinski II], or Chapters 9.5.3 and 9.5.4 of [GSW II].)

HW9 (due Thu, Nov 8): Problems 7.4, 7.11, 7.13 (pp. 292-295), 6.1 and 6.2 (pp.244-245 of [BBS]).
IMPORTANT CORRECTION: While the first three problems (7.4, 7.11, 7.13) are indeed due on Thu Nov 8, the remaining two will only be due a week later, on Thu Nov 15 (together with one additional problem, to be announced on Thu Nov 8).

HW10 (due Thu, Nov 15): The two left-over problems from last week (6.1 and 6.2), plus Problem 6.8 (page 246 of [BBS]).

HW11 (NOTE: this assignment is due in two weeks, on Thu, Nov 29): Problems 6.9 (p. 246), 5.9, 5.11 and 5.13 (p. 186 of [BBS]). Also, this assignment represents the last homework of this semester.

horava@berkeley.edu