Physics 234B: String Theory II

Spring 2008

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Basic Info

Instructor: Petr Hořava (email: horava@berkeley.edu)
Offices - campus: 401 Le Conte Hall; LBNL: 50A-5107.

This course is a continuation of 234A, focusing on the nonperturbative structure of string theory, and its implications. The Department's official syllabus for this new 234A/B sequence can be viewed here (for 234A: String Theory I), and here (for 234B: String Theory II).

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),

and also the newly published

E. Kiritsis, String Theory in a Nutshell (Princeton U.P., 2007).

However, since the material covered in this course is very modern and recent, we will have to make frequent detours into extra material, using arXiv review papers, and sometimes J. Polchinski's String Theory (in particular, Volume II). For low-energy supergravity, Green-Schwarz-Witten is also a useful source, even though it does not cover the modern duality developments.

In the Spring semester, we will cover five main themes, with approximately three weeks per theme:

I. String-string dualities, M-theory. (In other words, examples of "gravity-gravity dualities".) Spacetime effective supergravities; the BPS argument; string-string S-duality of Type IIB strings; Type I/heterotic duality; strongly coupled heterotic E8 x E8 and M-theory.
II. Black holes, black branes and their entropy. Bekenstein-Hawking entropy; statistical mechanics of black-hole entropy in string theory; holography; the OSV conjecture and topological strings.
III. Towards nonperturbative definitions of string/M-theory. Matrix models for the bosonic strings, Type 0 strings and noncritical M-theory; M(atrix) theory and DLCQ; (open) string field theory and Sen's conjectures.
IV. AdS/CFT correspondence. Gauge-gravity dualities; N=4 SYM/Type IIB on AdS_5; AdS_3/CFT_2; away from maximal supersymmetry; away from conformal invariance.
V. Recent developments and open questions. Topics include: AdS/QCD and the dynamics of the quark-gluon plasma; strings out of equilibrium; positive cosmological constant, cosmology and inflation in string theory; the landscape of vacua (and the swampland idea).

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

HW1 (due Thu, Feb. 7): Problems 8.4, 8.7 and 8.8 of [BBS] (page 352).

HW2 (due Thu, Feb. 21): Problems 8.9, 8.10 and 8.13 (pages 352-353), Problem 9.16 (page 455) of [BBS]. Additionally, in the discussion session on Thu. Feb. 14 we will take a closer look at the low-energy effective action of heterotic M-theory in eleven dimensions, and the students are advised to read the two original papers on this subject, hep-th/9510209 and hep-th/9603142, as their preparation for that discussion session.

HW3 (due Thu, March 6): Problems 11.6, 11.9, 11.11 and 11.14 of [BBS] (pages 608-9).

HW4 (due Thu, March 20): Two problems from [BBS]: 12.2 and 12.7 (p. 686). The third and final problem can be found in two "nutshell" places -- either as Problem 14.14 on p. 500 of [E. Kiristis, String Theory in a Nutshell], or as Problem VII.4.6 on p. 390 of [A. Zee, Quantum Field Theory in a Nutshell]. If you do not have access to either of those two books, the assignment of the problem is simple: Imagine integrating over all components of an NxN hermitean matrix M. Using a unitary group element U, you can diagonalize M, as M=ULU^{-1}, where L is a diagonal matrix: L=diag(l_1,...l_N). Perform the change of variables from M to U and l_1,...l_N in the integration measure, and show that the jacobian is given by the famous "Vandermonde determinant." Preferrably, derive this jacobian by using the Faddeev-Popov procedure.
In the discussion session on Thu March 13, we will discuss hep-th/0508024 (and possibly one of the follow-up papers, hep-th/0512325), on noncritical M-theory in 2+1 dimensions.

horava@berkeley.edu