Siegel's lectures, PHY 623, S'21

What are strings good for?

High-energy scattering: They're the only workable (although flawed) models of Calculations use perturbation theory, which produces much more calculable results than nonperturbative methods (@ least in > 2 dimensions), & for high energy (cross sections), not just low (masses, couplings, effective potentials). (An intermediate case is perturbative QCD, which uses large longitudinal momenta to calculate perturbative factors, & small transverse momenta to limit curve-fit nonperturbative factors.)

String scattering

topologyin subsectionsbackground material & homework
graph topology
  • P−V = L−1
VC2 (last ⅕)
1/Ncolor expansion
  • color loops
  • Euler number
  • flavor
VIIC4
worldsheet topology
  • duality
  • tadpoles
  • open→closed
XIA2XIA2.1 (due 3/19)
particle propagatorsIIIA1 (Dirac δ), IIIB (classical), VA3 (nonrelativistic)
  • proper time
  • iε ℞
  • energy sign
VB1VB1.1 (due 3/19)
1st-quantized particle graphs
  • Schwinger parameters
  • 1st-q action
VC8
worldsheet latticesVA5,VB4 (Wick rotation)
  • discrete worldsheet
  • string action
  • preon propagators
XIA7 (1st ½)XIA7.1 (due 3/22)
particle scattering
1st-q S-matricesIIIB3 (background fields), VA4 (nonrelativistic)
  • perturbation
  • interaction picture
  • Green function
  • loops
VIIIC5VA4.2 (due 3/22)
Γ functions
  • Schwinger parametrization
  • Beta function
VIIA2VIIA2.2,3, VIIC2.2 (due 3/26)
Coulomb scatteringIA4 (Mandelstam variables), VA2 (JWKB)
  • eikonal approximation
  • strong coupling
  • infrared
VIIA6 (2nd ½)VIIA6.2 (due 3/26)
string trees
Regge behavior
  • ladders
  • complex angular momentum
  • duality
XIA1XIA1.2 (due 3/29)
open trees
  • 4 tachyons
  • limits
  • higher-point
XIB6XIB6.2 (due 3/31)
closed trees
  • Schwinger parameters
  • 4 tachyons
  • open factorization
XIB7XIB7.1,2 (due 4/5)
ghosts
measure
  • vacua
  • Sp(2)
XIB8XIB8.2,3 (due 4/5)
vertex operators
  • BRST
  • massless vector
XIB9XIB9.1 (due 4/7)
string loops(as time permits)
partition function
  • integration measure
  • ghosts
XIC1
Jacobi Θ functionsVIIB5 (bosonization)
  • bosonization
  • symmetries
  • phase transition
XIC2XIC2.1 (due 4/9)
Green function
  • periodicity
  • SL(2,Z)
XIC3XIC3.1 (due 4/12)
open
  • poles
  • annulus
  • Möbius strip
  • group theory
XIC4XIC4.1 (due 4/14)
closed
  • SL(2,Z)
  • fundamental domain
  • divergences
XIC5