PHY 622 & 623 String Theory I & II

F'18, MWF 9:00-53 (ESS 069) — S'19, MWF 10:00-53

M. Roček, W. Siegel, P. van Nieuwenhuizen

office consultation available on request

This is a two-semester course. The course is taught by all of us; we sit in each other's lectures, and encourage discussions with students.

String theory is a vast subject, so it is not possible to cover all areas. We give simple introductions to the main areas; the lectures are self-contained. We do not use phrases like "It can be shown that...", but rather do all derivations and calculations explicitly.

This year we will begin teaching a revised version of the string course. As such, the following is a tentative description, subject to revision. The course will be more self-contained, and thus more introductory.

Grading: S/U

Grading is S/U, determined completely by the final exam, which is part written & part oral. There will also be frequent homeworks, mainly for you to monitor your progress.

Textbook: none

Free typed notes will be distributed.

Prerequisites: none

There are no prerequisites, other than a good undergraduate education. (Of course, any familiarity with core-course material will make life easier.)

First semester

The subject matter will go something like:

  1. Why strings? What are strings? (MR)
  2. 1st-quantization & spectrum
    1. Klein-Gordon scalar particle in all dimensions (MR)
      1. worldline gravity
      2. 1st-quantization: Klein-Gordon equation
    2. bosonic string (MR)
      1. worldsheet gravity: Weyl scale
      2. 1st-quantization: spectrum
    3. Dirac spinor particle in all dimensions (PvN)
      1. worldline supersymmetry
      2. worldline supergravity: Noether currents
      3. 1st-quantization: Dirac equation
    4. Ramond-Neveu-Schwarz spinning string (PvN)
      1. worldsheet supersymmetry
      2. worldsheet supergravity
      3. 1st-quantization: spectrum
  3. supergravity
    1. gravity in all dimensions, coupling to Dirac spinor (PvN)
      1. vielbein & local Lorentz symmetry
      2. Lorentz connection & covariant derivative
    2. 4D supergravity (PvN)
    3. higher-dimensional supergravity (MR)
      1. 11D supergravity
      2. dimensional reduction
      3. 10D supergravity: Types I, IIA & B
    4. some solutions of supergravity (MR)
      1. branes
      2. other compactifications
  4. Anti-de Sitter/Conformal Field Theory correspondence -- an introduction (WS)
    1. superconformal groups
      1. conformal group
      2. supergroups & superconformal groups
      3. coordinate cosets
    2. 4D classical conformal field theory
      1. N=4 super Yang-Mills
      2. superconformal coset & field strength
    3. 10D IIB supergravity on AdS₅×S⁵
      1. de Sitter & Anti-de Sitter spaces
      2. superAdS coset & field strength
    4. correspondence
      1. 1/N expansion
      2. definition
      3. boundary limit (group contraction) & lightcone gauge

Second semester

By the second semester we expect students to have completed the equivalent of the first semester of the core graduate courses, including quantum theory (while taking the second semester concurrently). The following outline is even more tentative, depending on how the first semester of the revised course goes.
  1. AdS/CFT that didn't fit in the 1st semester (WS)
  2. more supergravity (MR)
    1. more solutions of supergravity
      1. branes
      2. other compactifications
    2. supergravity dualities
      1. T-duality: Buscher rules
      2. S-duality: weak ↔ strong coupling
  3. Becchi-Rouet-Stora-Tyutin charge: covariant quantization
    1. constrained systems
    2. strings
  4. worldsheet (super)conformal quantum "field theory"
    1. worldsheet conformal symmetry
    2. 1 "loop" on worldsheet: D = 26 (bosonic) or 10 (spinning)
    3. bosonization
  5. Green-Schwarz approach
    1. triality: Ramond-Neveu-Schwarz ↔ Green-Schwarz
    2. superparticle
    3. superstring
  6. scattering amplitudes
    1. worldsheet symmetries
    2. Regge theory
  7. tree graphs
    1. particles
    2. bosonic strings
  8. heterotic string

On-line lecture notes, etc.

van Nieuwenhuizen



University-required statements
These statements are required in all University syllabi. (They are the same in all course syllabi, so just read it once.)