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2017

A Numerical Approach to Virasoro Blocks and the Information Paradox

Chen, Hongbin, Hussong, Charles, Kaplan, Jared et al.

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We chart the breakdown of semiclassical gravity by analyzing the Virasoro conformal blocks to high numerical precision, focusing on the heavy-light limit corresponding to a light probe propagating in a BTZ black hole background.

In the Lorentzian regime, we find empirically that the initial exponential time-dependence of the blocks transitions to a universal $t^{-\frac{3}{2}}$ power-law decay.
For the vacuum block the transition occurs at $t \approx \frac{\pi c}{6 h_L}$, confirming analytic predictions.
In the Euclidean regime, due to Stokes phenomena the naive semiclassical approximation fails completely in a finite region enclosing the `forbidden singularities'.

A Numerical Approach to Virasoro Blocks and the Information Paradox · Around

Built on

S. Ferrara, A. Grillo, and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys
1973
Earlier work this paper cites.
A. M. Polyakov, “Non-Hamiltonian Approach to the Quantum Field Theory at Small Distances,” Zh.Eksp.Teor.Fiz
1973
Earlier work this paper cites.
A. Zamolodchikov, “Conformal Symmetry in Two-Dimensions: An Explicit Recurrence Formula for the Conformal Partial Wave Amplitude,” Commun.Math.Phys
1984
Earlier work this paper cites.
A. B. Zamolodchikov and V. A. Fateev, “Disorder Fields in Two-Dimensional Conformal Quantum Field Theory and N=2 Extended Supersymmetry,” Sov. Phys. JETP
1986
Earlier work this paper cites.
J. L. Cardy, “Operator Content of Two-Dimensional Conformally Invariant Theories,” Nucl.Phys
1986
Earlier work this paper cites.
A. Zamolodchikov, “Conformal Symmetry in Two-dimensional Space: Recursion Representation of the Conformal Block,” Teoreticheskaya i Matematicheskaya Fizika
1987
Earlier work this paper cites.
T. Guhr, A. Muller-Groeling, and H. A. Weidenmuller, “Random matrix theories in quantum physics: Common concepts,” Phys. Rept
1998
Earlier work this paper cites.
J. M. Maldacena, “Eternal black holes in anti-de Sitter,” JHEP
2003
Earlier work this paper cites.
J. Teschner, “A Lecture on the Liouville vertex operators,” Int. J. Mod. Phys
2004
Earlier work this paper cites.
A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe, “Local bulk operators in AdS/CFT: A Boundary view of horizons and locality,” Phys.Rev
2006
Earlier work this paper cites.
P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP
Original
2007
Earlier work this paper cites.

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R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP
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2008
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