Classical Effective Field Theory (CLEFT)

1. Classical Effective Field Theory (CLEFT) Barak Kol Hebrew University - Jerusalem Bremen, Aug 2008 • Based on hep-th’s • 0712.2822 – caged w. Smolkin • 0712.4116 – PN w. Smolkin • 0804.0187 - BH deg of freedom • Outline • Domain of applicability • Brief review of results • Example: 1st Post-Newtonian order • Discussion

2. Domain of applicabilityGeneral condition Consider a field theory with two widely separated scales r0<<L See solutions perturbatively in r0/L.

3. Matched Asymptotic Expansion (MAE) Two zones. Bdry cond. come from matching over overlap. Near: r0 finite, L invisible. Far: L finite, r0 point-like. Effective Field Theory (EFT) Replace the near zone by effective interactions of a point particle Two (equivalent) methods

4. “Far” “Near” Applications • Born-Oppenheimer • Caged BHs • Binary system • Post Newtonian (PN) • Extreme Mass Ratio (EMR) • BHs in Higher dimensions • Non-gravitational Born-Oppenheimer approximation(1927) 0+1 Field theory Compute Ψe w. static nuclei and derive the effective nuclear interactions. In this way the EFT replaces the near zone by effective interactions

5. r0 L Near Far Caged Black Holes Effective interaction: field quadrupole at hole’s location induces a deformation and mass quadrupole

6. Binary system • The search for Gravitational waves is on: LIGO (US), VIRGO (Italy), GEO (Hannover), TAMA (Japan) • Sources: binary system (steady), collapse, collision • Dim’less parameters For periodic motion the latter two are comparable – virial theorem

7. Post-Newtonian Small parameter v2 Far zone Validity always initially, never at merger Extreme Mass Ratio m/M if initially, then throughout

8. Higher dimensional black objects Near zone Higher d ring Emparan, Harmark, Niarchos, Obers, Rodrigues

9. Non-gravitational • Electro-statics of conducting spheres • Scattering of long λ waves • Boundary layers in fluid dynamics • More…

10. Brief review of results • Goldberger & Rothstein (9.2004) – Post-Newtonian (PN) including 1PN=Einstein-Infeld-Hoffmann (EIH) • Goldberger & Rothstein (11.2005) BH absorption incorporated through effective BH degrees of freedom • Chu, Goldberger & Rothstein (2.2006) caged black holes – asymptotic charges

11. Caged BH’s and CLEFT BK & Smolkin 12.07 • CLEFT = CLassical Effective Field Theory, no i’s, no ‘s • NRG decompostion (=Non Relativistic Gravitation, which is the same as temporal KK reduction)

12. Definition of ADM mass in terms of a 0-pt function, rather than 1-pt function as in CGR CGR US • Rotating black holes

13. Post-Newtonian approx. Damour, Blanchet, Schafer • NRG decompostion terms Reconstructed EIH and following Cardoso-Dias-Figueras generalized to higher dimensions BK & Smolkin 12.07b

14. BH degrees of freedom • Physical origin of eff. deg. of freedom? • Near horizon fields (notably the metric) • delocalized through decomposition to spherical harmonics

15. EIH in CLEFT • Newtonian two-body action • Add corrections in v/c • Expect contributions from • Kinetic energy • Potential energy • Retardation

16. Feynman rules x EIH in CLEFT Action φ Ai

17. Feynman diagrams

18. Detailed calculation of retardation

19. Summary Exciting new theoretical tool • wide applicability • Efficient • Insight into divergences, regularization and renormalization in Quantum Field Theory

20. Challenges Renormalization and counter-terms within CLEFT. 1/ε→? Black hole effective action Open questions 2PN extend the 1PN (EIH) to reproduce the2PN result. Post-Minkowski separation much larger that Schw radii, but velocities are not assumed small (see Schafer) More…