PHY 621, Advanced Quantum Field Theory

The content of the course changes from year to year. This semester the topic will be

Mostly supersymmetry

1. simple & extended
2. Poincaré, anti-de Sitter, conformal
3. mostly superspace: off-shell, lightcone, twistor
4. actions & supergraphs
5. possibile additional topics: super-instantons, supergravity

Outline

1. Non-super
   1. spinor notation
   2. nonlinear σ-models & cosets
   3. projective lightcone: conformal, (anti-)de Sitter, Poincaré
   4. operators: symmetry generators & covariant derivatives
   5. covariant differentials & finite differences; integration measure
   6. spinor representations for cosets
   7. twistors & lightcone
2. Supersymmetry
   1. supergroups
   2. supertwistors
   3. superspaces: chiral & projective
3. N=1 superspace
   1. free theories: actions & components
   2. scalar multiplet
   3. vector multiplet: covariant derivative & prepotential
   4. extended in terms of N=1
4. N=1 supergraphs
   1. scalar multiplet
   2. vector multiplet
5. N=2 superspace
   1. scalar multiplet
   2. vector multiplet
6. N=2 supergraphs
7. N=4? AdS/CFT?

Texts

• Books: Fields, Superspace
• Preliminary course notes: These are still being written (so if you print, do just the pages you need immediately). The stuff should be OK through "Simple superspace", which will come from Fields, & take a significant fraction of the semester.
  • 1/25: Added a sentence to the end of p. 4. More stuff in the Hyperspace section (which isn't worth reading yet).
  • 1/26: Added to the sentence @ the end of the subsection on p. 17. More Hyperspace (still 3 months away).
  • 1/27: More Hyper.
  • 1/28: Added sentences to the middle of p. 13, (what's now) the end of p. 14, & the end of the subsection on p. 17. That pushed things around a bit.
  • 1/29: Added a couple of parenthetical remarks to the beginning of the subsection on p.3. More Hyper.
  • 2/11: Added an extra paragraph to the top of page 4 (pushing later pages ahead 1 page). More Hyper.
  • 2/12: Added an extra paragraph & exercise in the middle of "Charge conjugation".
  • 2/17: Added an exercise @ the end of p. 12.
  • 2/19: Added comments to bottom of p. 8 about minimum number of θ's.
  • 2/23: Rewrote some of the first subsection, Group coordinates (pp. 2-5), especially the last page, about wave functions, where everything was backwards.
  • 2/24: Added a little more to the end of Group coordinates, in the new subsection Wave functions and spin.
  • 3/3: tr → str @ bottom of p. 16. 2 str I → str I @ bottom of p. 19; a little more explanation of N=2 example there. Fixed equations of motion in On-shell superfields, with new exercise (again pushing things around a bit).
  • 3/5: Modified the discussion of r & r̄ on p. 15. On the bottom of p. 20, the Pauli-Lubański equation doesn't require superhelicity 0. Modified the end of the exercise on p. 23. Added to the discussion of full-index twistor coordinates near the bottom of p. 24, & @ the end of the (new) p. 25.
  • 3/8: More stuff on superhelicity on pp. 23 & 25.
  • 4/14: Reorganized the scalar hypermultiplet stuff a bit. Added stuff to "Other coordinates" & "Vector hypermultiplet action". Put a few preliminary equations into the "Quantum" part of Hyperspace.
  • 4/15: Modified the classical hyperspace stuff a little; did most of the quantum.
  • 4/16: More modifications to Hyperspace: some discussion of N=4 @ the end of Field equations, a free component analysis @ the end of Action for Vector hypermultiplet, more elaboration on gauge fixing for Vector hypermultiplet, other small things. Still needs fixing of signs, factors of 2, etc.
  • 4/19: Superconformal invariance @ the end of Vector hypermutiplet Action. Feynman rules @ the end of Quantum Vector hypermultiplet.
  • 4/20: More @ the end of Quantum Scalar hypermultiplet. Some preliminary N=4 stuff.
  • 4/21: Hypergraph examples.
  • 4/22: Fixed a few errors/omissions in Other coordinates, and Vector Hypermultiplet Coupling & Action. More on AdS/CFT.
  • 4/23: More AdS/CFT.
  • 4/26: More AdS/CFT.
  • 4/27: More @ the end of AdS/CFT. Fixed the stuff in Quantum Scalar hypermultiplet.
  • 4/29: More on N=4 Tree. Fixed Quantum Vector hypermultiplet & Hypergraphs.
  • 5/3: Fixed the typos in Propagator and Tree. Added more to 10D field equations.
  • 5/4: More AdS/CFT.
  • 5/10: Final (?) corrections, to 10D field equations and Correspondence.

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