Upload
others
View
5
Download
0
Embed Size (px)
Citation preview
Classical dynamics from spinors
Higgs Centre for Theoretical Physics,
The University of Edinburgh QCD meets Gravity VI, 30/11/20
With Alfredo Guevara, Alex Ochirov, Donal O’Connell and Justin Vines
Outline
1. The worldline NJ shift
2. From worldsheets to spinors
▪ Electrodynamics
▪ Gravity
3. Electric-magnetic duality
▪ Kerr-Taub-NUT
4. Discussion
Worldline NJ shift
Take sheet coordinates 𝓏 𝜏, 𝜆 = 𝑟 𝜏 + 𝑖𝜆𝑎 𝜏 .
Worldsheet action → chiral Newman-Janis shift to worldline
Kerr
worldsheet:
Spinors in classical physics
NJ shifts natural for spinors:
Weyl:
Maxwell:
Exploit chiral splitting: spinor-helicity.
Newman & Janis, 1965
From worldsheets to spinors
Common structure:
Common basis:
Dynamical spinorsLittle group tensor
Arkani-Hamed,
Huang &
Huang, 2017
Particle dynamics encoded by spinors!
Spinor equations
𝑝 and 𝑎 form distinct little group irreps:
SymmetricSinglet state
Set 𝑎 = 0; must recover Lorentz force!
Example
Kerr scattering
Static Kerr background:
LO probe trajectory 𝑟1 𝜏 = 𝑏 + 𝑢1𝜏 :
Kerr probe:
Worldline NJ shift
Background NJ shift
Arkani-Hamed, Huang &
O’Connell, 2019Spin-spin scattering as easy as spin-static!
Impulse:
Δ𝑎𝜇 free.
Gravity
Linearised Kerr worldsheet:
→ spinor equations in gravity are
Worldsheet provides covariant meaning for trajectory’s NJ shift.
Connection spinor:
Porto, Rothstein; Levi & Steinhoff
EM duality for fields
Turn on magnetic charge for background field:
Huang, Kol, & O’Connell, 2019
+ Emond & Moynihan, 2020
→ simple maps between spinors:
Talbot, 1969 Kim & Shim, 2020
Einstein-Maxwell:
Maxwell:
EM duality for particles
∴ include phase rotation on spinors for particle:
Spinor equations for Kerr-Taub-NUT
Phase rotation for on-shell amplitudes:
→ EM duality for interactions!
Kerr-Taub-NUT scattering
Scatter off static Kerr-Taub-NUT background:
Background
NJ
from amplitudes: Emond, Huang, Kol,
Moynihan & O’Connell, 2020
Angular impulse easy. Difficult calculations from KTN metric!
Worldline dualityBackground duality
Worldline NJ
𝑤 = rapidity
KTN probe:
Impulse:
Discussion
• NJ shifts, EM duality natural for spinors → exploit to provide compact
description of dynamics of spinning + charged black holes.
• What are the spinor equations at higher orders?
• Angular impulse just as easy as impulse.
• Worldsheet actions = chiral splitting of spin couplings.
Spinor equations = chiral splitting of dynamics.
• Do the worldsheet symmetries constrain tidal 𝒪 𝐹2 or 𝒪 𝑅2 terms?
• Do the worldsheet action and spinor equations constrain the classical
Compton amplitude?
Kim & Shim, 2020
see Jung-Wook’s talk
see Michele’s talk
Next steps:
Results known for Taub-NUT at NLO
Also easier than amplitudes:
BM, O’Connell & Vines, 2019