Physics 234A: String Theory I -- Outline

Fall 2007

Unofficial Week-by-week Outline

Disclaimer: This outline is highly tentative, and the instructor reserves the right to change it randomly and with very little notice.

Week 1: I. Why strings?
Tue: Quantum field theory of brane fluctuations in ambient spacetime; Goldstone's theorem; critical dimension of the free scalar field;
Thu: Dual models, Regge trajectories, the Veneziano amplitude.
Week 2:
Tue: QFT of a free massless scalar in two dimensions; anomalous dimensions of composite operators.
Thu: Classical and quantum gravity on the worldsheet; Weyl symmetry.
Week 3: II. The bosonic string
Tue: Quantization: critical and noncritical strings, Liouville field; closed and open strings, conformal gauge, Virasoro constraints.
Thu: Faddeev-Popov procedure, ghosts, BRST symmetry.
Week 4:
Tue: String spectrum; old covariant quantization versus BRST; spacetime gauge invariance, the critical dimension.
Thu: Lightcone gauge; basics of 2d CFT, with simple examples; operator product expansions (OPEs); state-operator correspondence; vertex operators.
Week 5:
Tue: String perturbation theory; quantum field theory on Riemann surfaces; moduli spaces; general n-point amplitudes.
Thu: Examples of tree-level amplitudes; n-point amplitude on the sphere and the disk; path integral evaluation; the Veneziano amplitude (and, almost, the Virasoro-Shapiro amplitude).
Week 6:
Tue: One-loop partition function in CFT and in string theory; modular invariance; classical solutions of string theory versus 2d CFTs.
Thu: More CFT; Verma modules; Kac and minimal models; classification of c = 1 CFTs; orbifolds.
Week 7: III. Superstrings
Tue: More symmetry on the worldsheet: Kac, Moody, Sugawara and others; coset models, WZW Lagrangian. More local symmetry on the worldsheet: worldsheet supergravity, superstrings.
Thu: Worldsheet superspace formulation; superstrings in superconformal gauge; Neveu, Schwarz and Ramond; GSO projection.
Week 8:
Tue: BRST quantization, superghosts, superconformal field theory (SCFT); Type 0 and Type II strings.
Thu: Bosonization of the superghosts; Green-Schwarz (GS) formalism: Spacetime supersymmetry.
Week 9: IV. Heterotic strings
Tue: Green-Schwarz formulation: continuation.
Thu: Heterotic strings; NSR fermionic formulation; classification of modular invariant heterotic models in ten dimensions.
Week 10:
Tue: Compactification on tori; the bosonic formulation of the heterotic string; even self-dual lattices; Narain compactifications.
Thu: V. D-branes
Open strings, T-duality, Ramond-Ramond fields, D-branes.
Week 11:
Tue: RR fields and their electric and magnetic couplings to branes; stable D-branes in Type IIA, Type IIB theory; orientifolds, Type I, Type I'; charges and half-BPS states.
Thu: Unstable D-branes; brane-antibrane systems; open-string tachyon condensation; D-branes as topological defects in tachyon condensates; D-brane charges and K-theory. The Born-Infeld action.
Week 12:
Tue: Worldvolume action on D-branes (continuation); open-closed string duality, one-loop amplitudes; worldsheet and spacetime calculation of the tension (and charge) of D-branes (and orientifold planes).
Thu: Green-Schwarz anomaly-cancellation mechanism: Heterotic, Type I, Type IIB anomaly cancellation.
Week 13:
Tue: Boundary-state and crosscap-state formalism.
Week 14: VI. Classical solutions of string theory
Tue: Examples of exact CFTs as solutions of string theory; Calabi-Yau compactifications.
Thu: Conditions of unbroken supersymmetry in string backgrounds; covariantly constant spinors, implications for geometry.
Week 15:
Tue: The two-dimensional dilaton Schwarzschild black hole as a gauged WZW model.
Thu: Strings at finite temperature; Hagedorn behavior; string gas cosmology.