Physics 234A: String Theory I -- Outline

Fall 2008

Week 1: Introduction
Thu: Organization of the course, outline of main themes.
Week 2: I. Why strings?
Tue & Thu: Strings and unification; strings from a historical perspective; special properties of strings in the "democracy of branes"; four "coincidences" in 1+1 dimensions: (1) scalars at the critical dimension, (2) gravity at its critical dimension, (3) infinite-dimensional conformal symmetry (implying target Einstein equations!), (4) classification of compact surfaces by genus vs. the existence of string perturbation theory.
Fri discussion: The Veneziano amplitude.
Week 3: II. The bosonic string
Tue & Thu: The Nambu-Goto vs. Polyakov action; critical and noncritical strings; worldsheet gauge symmetries; open-string boundary conditions; covariant canonical quantization of the free string.
Fri discussion: Goldstone's theorem; quantum field theory and renormalization of a free scalar field in two dimensions.
Week 4:
Tue & Thu: Covariant quantization and the spectrum of free open and closed strings; absence of ghost states, critical dimension; light-cone quantization; worldsheet CFT.
Fri discussion: The best-kept secret of relativistic quantum field theory?
Week 5:
Tue & Thu: CFT in two dimensions; BRST quantization.
Fri discussion: HW1 solutions.
Week 6:
Tue & Thu: String perturbation theory; scattering amplitudes.
Fri discussion: No discussion.
Week 7: III. Superstrings
Tue & Thu: Worldsheet supersymmetry; NSR formalism; spectrum of free superstrings; critical dimension, super-Virasoro, SCFT.
Fri discussion: HW2 solutions.
Week 8:
Tue & Thu: GSO projection; Type I, IIA, IIB theory in ten dimensions; spacetime supersymmetry and the Green-Schwarz formalism.
Fri discussion: Continuation of the HW2 discussion.
Week 9: IV. D-branes
Tue & Thu: Introduction to D-branes. Guest lecturer: Professor Ori Ganor.
Fri discussion: No discussion.
Week 10:
Tue & Thu: Properties of D-branes; DBI action; boundary and crosscap states; D-brane tension.
Fri discussion: HW3 solutions.
Week 11: V. Heterotic strings
Tue & Thu: (Some leftovers from the D-brane chapter: Orientifold tension; brane-antibrane systems; classification of stable D-branes by K-theory.)
Preview of S-dualities: the D-string in Type IIB superstring theory. The D-string of Type I superstring theory. Worldsheet theory of the heterotic strings; spacetime non-Abelian symmetries from worldsheet current algebras.
Fri discussion: HW4 solutions.
Week 12:
Tue: No lecture - Veterans' Day.
Thu: Heterotic strings in the fermionic formulation.
Fri discussion: Continuing with HW4 solutions.
Week 13: VI. Selected topics & applications of string theory
Tue & Thu: Spacetime effective supergravity actions; anomalies and their cancellation; the Green-Schwarz mechanism. String-string dualities and M-theory.
Fri discussion: HW5 solutions.
Week 14:
Tue: M-theory and nonperturbative string dualities. Type IIA from M-theory on a circle. Heterotic M-theory.
Thu & Fri: No lecture/discussion (Thanksgiving)
Week 15:
Tue & Thu: Type IIB SL(2,Z) duality from M-theory on a torus. A glimpse of Calabi-Yau compactifications; phenomenology of weakly coupled heterotic string and of heterotic M-theory.
Fri discussion: HW 6 solutions.
Week 16:
Tue: Why strings? The large-N expansion in quantum field theory; AdS/CFT duality. Type IIB on AdS5xS5 and N=4 super Yang-Mills; deriving the correspondence from the decoupling limit of N D3-branes.

horava@berkeley.edu