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Conformal Bootstrap, Universality and Gravitational Scattering
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abstract
We use the conformal bootstrap equations to study the non-perturbative gravitational scattering between infalling and outgoing particles in the vicinity of a black hole horizon in AdS. We focus on irrational 2D CFTs with large $c$ and only Virasoro symmetry. The scattering process is described by the matrix element of two light operators (particles) between two heavy states (BTZ black holes). We find that the operator algebra in this regime is (i) universal and identical to that of Liouville CFT, and (ii) takes the form of an exchange algebra, specified by an R-matrix that exactly matches with the scattering amplitude of 2+1 gravity. The R-matrix is given by a quantum 6j-symbol and the scattering phase by the volume of a hyperbolic tetrahedron. We comment on the relevance of our results to scrambling and the holographic reconstruction of the bulk physics near black hole horizons.
Forward citations
Cited by 3 Pith papers
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QG from SymQRG: AdS$_3$/CFT$_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow
A framework called SymQRG identifies 3D quantum gravity as the symmetry-preserving RG flow of 2D CFTs, realized discretely by U_q(SL(2,R)) 6j symbols.
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A Holographic Map from AdS$_3$ to CFT$_2$
Semiclassical pure AdS3 gravity states, labelled by fixed-area geodesic networks, are mapped to CFT2 primary states whose wavefunctions are networks of OPE coefficients.
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Global Symmetry and Maximal Chaos
For arbitrary-high-charge operators in a system with a global symmetry and chemical potential, the chaos bound weakens to 2πT/(1-|μ/μ_c|), where μ_c is the critical chemical potential.
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