Barak KolHebrew University - Jerusalem

Jun 2011, Milos

Outline

• set-up

• puzzles and previous work

• The new effective theory

• Results

Based on arXiv: 1103.5741 BK

W. Goldberger – early collaboration

w/ M. Smolkin - related work

Set-up

Ultra relativistic (massless) weak scatteringThe parametersGeneralizations: Possible interactions, dimensions, masses

Planckian scattering

• Intuitive condition for black hole creation

• Quantum black holes

The perturbative regime

• The small parameter

• Objective: – trajectories and especially – scattering angle

: 1cmGE

b

Backgroundpuzzles

• ‘t Hooft – natural probe for quantum gravity

- 4d Gravity simplifies for light-like

- reminiscent of 3d branch cuts• w. Dray (1985) jump at shock

wave• (1987) Classical dominance

including sub-planckian b!• Relation with Veneziano

amplitude

Backgroundpuzzles

• Amati, Ciafaloni, Veneziano (1987,…,2008)

string theory as quant. Grav.Eikonal approx, effective theory “H” correction diagram, dealing

with IR div• Verlinde2 (1992) –

“topological field theory”• Giddings• Computer simulationsChoptuik-Pretorius 2009Sperhake et al (2010)

Post-Newtonian approximation

• Definition: relativistic correction to slow motion in flat space-time

i.e. Mercury around the sun, binary system in adiabatic inspiral

• Small parameter v2/c2 ~GM/R <<1

• The EFT approach r0=2GM<<R

• The instantaneous

spatial propagator

Damour, Blanchet, Schäfer

2 2 2 20

1 1 1

k k k k

0T R k k

Goldberger, Rothstein(2004)

Grav Field Re-definitionStationary (t-independent)

problem• Technically – KK

reduction over time• “Non-Relativistic

Gravitation” - NRG fields

Non-linear definition

Physical interpretation of fields

• Φ – Newtonian potential

• A – Gravito-magnetic vector potential,

similar poles attract

0712.4116BK, Smolkin

2 2 / 32 2

2 2 22 13 4 3

2

, ,

1exp

16

i

d

ij

ii i j

ddd

ij

d

h

ds e dt dx e dx dx

S dt dx RG

A

A

F

Recovering time dependence

1009.4116BK, Smolkin

Non-orthonormal frame

1PN: 0712 Kol Smolkin2PN: 0809 Gilmore Ross3PN: 1104 Sturani-Foffa

Difficulty in importing PN ideas

Each particle unperturbed motion is

invariant under a different light-cone coordinate z+, z-.

Relation to other work presented at this meeting

• Holographic renormalization (Papadimitriou)

• Hydrodynamics and gravity (Y. Oz, A. Strominger, K. Skenderis)

Related concepts

Vought_V-173 “flying pancake” experimental aircraft tested 1942-7

Related concepts

Beat 1 Beat 2 Beat 3

Mahler symphony no. 2, 3rd movementConducted by L. Bernstein

“St. Anthony Preaches to the Fishes”

The effective theory

4

,

1; , [ ]

16

, /2

A A AA R L

I

A A A

S g X e d x R g SG

pS X e ds g X X X e

Recall the set-up..

The action

Field lines

“flying pancake”

• Imagine the field lines emanating from a point charge

• At rest – spherical• When ultra relativistic

– Lorentz contracted longitudinally– pancake-shaped transversely– Aichelburg-Sexl

• “The particle carries a pancake on its nose”

Sudden interaction

• The moment of passing – when the pancakes coincide

• Interaction localized in z,t

• Eq of motion are sudden, algebraic recursion rather than differential

Mahler’s 2nd

The propagator

2 k+ k- is a quadratic perturbation

The momentum transfer

k k k

~ 1cmG Ek

k b

2 2 2

1 1 1

2k k k k k

2cmp G E k

Field decomposition

• Dimensional reduction onto transverse space

à la Kaluza-Klein

• Gab are (transverse) scalars. Analogous to the Newtonian potential.

G++ couples to R, G-- couples to L.

• Aai are two (transverse) vectors.

couple to mass current in the transverse plane.• Spin is dipole charge for vectors.

2

, , , , , , ,

( )( )

aab i ij

a ba

ab i j ij

i b j i j

g a b i j x y

ds dz dx dz dx

G A g

G A A xg d dx

BK 2010

Whole action

Extrinsic curvature

deWitt metric

BK (2011)Yoon (1996,99)

Results1st order and momentum transfer

Ultra-relativistic dynamics

• “Light-cone”/ “infinite momentum frame”• A particle has a total of 3 degrees of

freedom• 2 transverse (ordinary) degrees of

freedom• p+ plays the role of mass, z+ is time • z- is a 1st order ODE – constraint – half dof• e the world-line metric, or equiv z+ is the

other half

DiracWeinbergSusskind

2-body effective actionScalar interaction

For scalar→gravitational change e factors, add non-linear blik vertices

2nd order

Mass shall

Energy unchanged in CM frame

Improved “renormalization”

• “Ordinary” initial conditions for scattering at t=-∞

• Specify initial conditions at nearest approach “t=0”pretending to know them.

Higher symmetry: parity in the pert theoryEvolve both forward and backward in time to

eliminate the t=0 conditions

Interaction duration – 3rd order

• Obtain a term of type

• ε2 c3/c1 estimates τ2, where τ is the (finite) duration

• We find τ≈ε b• This is consistent with the arc’s radius of

curvature being b, namely the center of force being at the other particle

31 3 ''p c s sc

BK2011 At d=4 there is a pole in dim. Reg.

Discussion

• We defined a classical effective field theory (CLEFT) - different from PN.

• Result: interaction duration resolved• Relation with eikonal approximation

Late 1960s, QFT context,

concept borrowed from optics –

an approximation of wave optics calculated on the basis of rays

Eikon=image in greek

Open questions

Non-conservation due to radiation:

Energy, momentum, angular momentum

Cylon raider from Battlestar Galactica

Darkness and Light in our region

ΕΦΧΑΡΙΣΤΟ! Thank you!