## 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:

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 -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 and
- 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.

Merisaid, on December 1, 2008 at 11:01 pmWhat’s up with the “…” in Siegel’s lectures? Did you fall asleep during your own advisor’s lecture!? How scandalous…

Index Guysaid, on December 1, 2008 at 11:04 pmπ

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