Day three starts with a slightly odd session (for me); one talk I am interested in followed by three I am not. I didn't finish writing my own talk yesterday, so I guess that works out for me.

What is the quantum nature of gravity? What is the high energy behaviour of graviton scattering amplitudes? Can these questions be answered just in Einstein gravity?

Well known that 2 to 2 graviton scattering violates (tree-level) unitarity at the Planck scale. The Wilsonian approach is that we integrate in new, weakly-coupled UV degrees of freedom to solve this problem. Classicalisation is based on instead "integrating in" strongly coupled objects, namely black holes, that already exist in the theory. Gravity protects itself. But to make this idea quantitative, need to better understand how black holes are formed in graviton scattering amplitudes.

Black hole

Is there a signal of non-perturbative BH physics in perturbative graviton scattering? Compute 2 to

Some technical details of the calculation. For many reasons, I'm not going to say anything about that here.

Result: for fixed

In string theory, old result that high-energy amplitudes have exponential fall off from heavy Regge states. Generalise this to large

Would loop level still be exponentially suppressed? Some arguments I didn't quite follow or find compelling, but main point seems to be that still need to do the calculation.

Collider searches for BHs split over direct searches or just looking at form factors; comments? Above the string scale, won't see BHs, so those searches need to be redone.

**9:00 am: "Black Hole Formation and Classicalization in Ultra-Planckian Graviton Scattering", Dieter Lust**What is the quantum nature of gravity? What is the high energy behaviour of graviton scattering amplitudes? Can these questions be answered just in Einstein gravity?

Well known that 2 to 2 graviton scattering violates (tree-level) unitarity at the Planck scale. The Wilsonian approach is that we integrate in new, weakly-coupled UV degrees of freedom to solve this problem. Classicalisation is based on instead "integrating in" strongly coupled objects, namely black holes, that already exist in the theory. Gravity protects itself. But to make this idea quantitative, need to better understand how black holes are formed in graviton scattering amplitudes.

Black hole

*N*-portrait is based on quantum BH identified as BE condensate of*N*gravitons. I saw Dvali (I think) give a talk on this at Planck four years ago, in Warsaw. The relevant features needed here is that*N*is large, so the gravitons are soft. The individual graviton coupling*α*is small, but there is a collective, 't Hoot-like coupling (*λ = α N*), that is equal to 1 in BHs. Also, the BH entropy comes from from the huge graviton degeneracy.Is there a signal of non-perturbative BH physics in perturbative graviton scattering? Compute 2 to

*N*scattering in large-*N*regime, in field theory. Compare string calculation. Find soft final gravitons unitarised by BHs, hard ones by string Regge states.Some technical details of the calculation. For many reasons, I'm not going to say anything about that here.

Result: for fixed

*λ*, 2 to*N*scattering amplitude exponentially*suppressed*with*N*! Due to enhancement by combinatorics offset by suppression by gravitational coupling. Further, we can observe that the suppression factor is the inverse of the BH entropy. This can be read as evidence that the*N*final state gravitons are indeed forming a (non-perturbative) BH in this (perturbative) calculation. Multiplying the perturbative amplitude by the BH entropy gives a function purely of the gravitational coupling, and*λ*= 1 is the cross-over point between weak coupling (unitary) and strong coupling (classicalisation).In string theory, old result that high-energy amplitudes have exponential fall off from heavy Regge states. Generalise this to large

*N*case. Find a low-energy regime that agrees with the field theory calculation, and a high-energy regime that differs. Then interesting results for unitarity when this string point is higher/lower than the BH formation point. Two points are equal at string/BH correspondence point.__Questions__Would loop level still be exponentially suppressed? Some arguments I didn't quite follow or find compelling, but main point seems to be that still need to do the calculation.

Collider searches for BHs split over direct searches or just looking at form factors; comments? Above the string scale, won't see BHs, so those searches need to be redone.

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