Physics 234A: String Theory I - Outline
Disclaimer: This outline is highly tentative, and the instructor
reserves the right to change it randomly and with very little notice.
Week 1: Introduction
Fri Aug 26: Organization of the course, outline of main themes;
strings and unification; strings from a historical perspective.
Week 2: I. Why strings?
Mon & Fri:
Special properties of strings in the "democracy of branes";
Goldstone's theorem; 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
Fri: Introducing the bosonic string. The Nambu-Goto vs. Polyakov
action; critical and noncritical strings.
Fri discussion: HW1 solutions. Renormalization of the free
scalar QFT in two dimensions.
Mon & Fri:
The large-N expansion in quantum field theory; gauge-gravity
Back to the bosonic string: worldsheet gauge symmetries; open-string boundary
conditions; covariant canonical quantization and the spectrum of the free
Fri discussion: HW2 solutions.
Mon & Fri: Absence of ghost states, critical dimension; light-cone
No discussion session in Week 5.
Mon discussion: HW3 solutions.
Mon: Worldsheet CFT; operator product expansions; conformal primaries,
weights/conformal dimensions; example: scalar-field CFT.
Classical solutions of string theory.
Because of a BCTP workshop on Friday, there is no lecture or discussion
Instead, there will be a make-up lecture on Monday of Week 7, at 11:10am.
Mon 11:10am: More examples of CFTs: minimal models, ghost
systems; WZW models; classification of c=1 CFTs.
Mon & Fri: Worldsheet path integral and gauge fixing; the Faddeev-Popov
procedure, ghosts; BRST quantization; examples: pointlike particle, bosonic
string, topological QFT and topological strings.
Fri discussion: HW 4 solutions.
Week 8: III. Superstrings
Mon & Fri:
Worldsheet supersymmetry; NSR formalism; spectrum of
free superstrings; super-Virasoro.
No discussion session in Week 8.
Mon & Fri: String (and superstring) perturbation theory; moduli
spaces. Modular group and modular invariance. GSO projection, Type O,
Type I and Type II superstrings. Topological Yang-Mills theory.
Fri discussion: HW 5 solutions.
Week 10: IV. D-branes
Mon & Fri: Strings in background fields; spacetime supergravity;
RR fields and their coupling to nonperturbative branes. T-duality for closed
and open strings; first appearance and basic definition of D-branes.
Fri: Make-up lecture, on spacetime supersymmetry and the Green-Schwarz
Mon & Fri:
Boundary and crosscap states; D-brane tension; orientifold tension;
brane-antibrane systems; stable D-branes and K-theory; DBI action.
Preview of S-dualities: the D-string in Type IIB superstring theory.
The D-string of Type I superstring theory.
Fri discussion: HW 6 solutions.
Week 12: V. Heterotic strings
Mon: Worldsheet theory of the heterotic strings; spacetime non-Abelian
symmetries from worldsheet current algebras. Heterotic strings in the
Mon & Fri: Spacetime anomalies and their cancellation; the
Green-Schwarz mechanism. String-string dualities and M-theory.
Fri discussion: HW 7 solutions.
Week 14: VI. Selected topics & applications
of string theory
Mon: M-theory and nonperturbative string dualities. Type IIA from
M-theory on a circle. Heterotic M-theory.
Mon & Fri: Type IIB SL(2,Z) duality from M-theory on a torus.
Rudimentary elements of Calabi-Yau compactifications. Phenomenology of
the weakly coupled heterotic string and of heterotic M-theory.
Fri discussion: HW 8 solutions.
Week 16: Review/outlook week
Back to the origins: Why strings? The large-N expansion
in QFT; AdS/CFT duality. Type IIB on AdS5xS5 and N=4 super Yang-Mills;
deriving the correspondence from the decoupling limit of N