Index Concordia

Strings

During the Fall 2008 I took the course on string theory taught by Professors Rastelli, Rocek, Siegel and van Nieuwenhuizen. Here is a rough outline of the topics discussed:

Weeks 01 02 & 03 (lectures by van Nieuwenhuizen) – Bosonic strings

  • Actions: Polyakov and Nambu-Goto form
  • Worldsheet metric: Virasoro constraint and symmetries
  • Symmetries of actions: Einstein, Weyl, Lorentz
  • Field equations and solutions: mode expansions, boundary conditions
  • Light-cone gauge and conformal gauge
  • Energy-momentum tensor of the worldsheet: Virasoro generators, commutation relations and other properties
  • Quantization: canonical, light-cone, covariant
  • Spectrum of the bosonic string: tachyonic, massless, massive states
  • Covariant quantization: gauge-fixing, ghost and antighost; Weyl ghost
  • BRST rules for the bosonic string, BRST charge and current, nilpotency and critical dimension, normal-ordering anomaly and intercepts

Weeks 03 04 & 05 (lectures by Rocek) – Spinning strings

  • Worldsheet spinors/spacetime vectors
  • Action and symmetries: superconformal symmetry, Einstein, Weyl
  • Worldsheet objects: metric, vielbein, gravitino as gauge field for local supersymmetry
  • Field equations and solutions: mode expansions, boundary conditions, zero-modes
  • Clifford vacuum, spectrum of open and closed spinning strings; Neveu-Schwarz and Ramond sectors and their tensor products
  • GSO projection operator, physical states; type IIA and IIB strings; d=10 supergravity coincidence
  • Covariant quantization of spinning string: ghost and antighost, gauge-fixing, mode expansions
  • BRST charge and current
  • Critical dimension

Weeks 06 & 07 (lectures by van Nieuwenhuizen) – Conformal field theory

  • Conformal transformations of fields
  • Complex coordinate basis, complex plane and cylinder
  • Normal ordering
  • Wick’s theorem and contractions
  • Operator product expansions
  • Propagators: string coordinates, ghosts, worldsheet spinors
  • Energy-momentum tensor as generator of conformal transformations
  • Schwartzian derivative
  • Conformal normal ordering
  • BRST charge and current in the conformal plane

Weeks 07 08 09 & 10 (lectures by Siegel) – Vertex operators and trees

  • Two-dimensional quantum field theory
  • Bosonization and fermionization
  • Vertex operators: integrated and otherwise
  • Picture changing

Week 11 (lectures by Rocek) – T-duality

  • T-duality for closed strings: winding and momentum states, compact dimensions
  • Spectrum
  • T-duality for open strings: Wilson lines, string charge
  • Mode expansions
  • T-duality and spinning strings

Weeks 12 13 14 15 (lectures by Rastelli) – D-branes and boundary state formalism

  • Boundary states: bosonic and fermionic
  • Duality between open- and closed-string channels
  • Born-Infeld term as worldvolume action for branes

The lectures on D-branes followed some notes that can be found online:

  1. hep-th/9912161
  2. hep-th/0005029

The Spring 2009 view the second part of this course.

Weeks 01 02 03 & 04 (lectures by Siegel) – Loop amplitudes

  • Regge theory and duality
  • Topology of interactions
  • First quantization of particles and scattering amplitudes
  • Background field method
  • Open and closed string propagators
  • Regge behavior of string amplitudes
  • Jacobi \Theta-functions and their properties
  • Partition function for loops
  • Cancellation of anomalies and divergences

Weeks 05 & 06 (lectures by van Nieuwenhuizen) – Heterotic strings

  • Lagrangian
  • Model with 16 scalars
  • Model with 32 fermions
  • Gauge symmetry of E_{8} \times E_{8} and SO(32)
  • Lattices
  • Vertex operator representation of simply laced Lie algebras

Weeks 06 07 08 09 10 (lectures by Rocek and van Nieuwenhuizen) – Supergravity, extended solutions and anomalies

  • Four-dimensional simple supergravity: field contents, action and symmetries
  • Eleven-dimensional supergravity: field contents, action, supersymmetry transformations, field equations
  • Supersymmetry backgrounds and BPS conditions
  • Explicit calculation of M2 brane solution
  • M5 solution
  • Near-horizon limit of solutions; superposition; smearing
  • Taub-NUT solution, KK6 solution, KK1 solution
  • Ten-dimensional supergravities: type IIB, IIA and I, field content, lagrangians,
  • Einstein and string frames
  • Ten-dimensional super Yang-Mills
  • Gravitational and gauge anomalies; cancellation
  • Extended solutions and the relations among them; ten-dimensional reduction
  • T-duality and the Buscher rules
  • Tension of branes

Weeks 12 13 14 15 (lectures by Rastelli) – Anti-de Sitter/Conformal Field Theory correspondence

  • String and field theory sides, symmetries, identification of parameters
  • Conformal group, correlation functions, representations
  • Geometry of anti-de-Sitter spacetime, Penrose diagrams, coordinate systems
  • Masses in gravity theory and conformal dimensions in the field theory side
  • Superconformal group and representations
  • Long, short and semi-short multiplets
  • Supergravity side
  • Correlation function

The lectures on adS/CFT followed roughly the first three chapters of MAGOO and also some of this article by Dolan and Osborn.

2 Responses

Subscribe to comments with RSS.

  1. Meri said, on December 1, 2008 at 11:01 pm

    What’s up with the “…” in Siegel’s lectures? Did you fall asleep during your own advisor’s lecture!? How scandalous…

  2. Index Guy said, on December 1, 2008 at 11:04 pm

    πŸ˜›

    At this point I have not outlined his lectures properly. πŸ˜‰ I should start doing that soon since the topics he discussed were among the most non-trivial.


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: