Two-dimensional conformal field theory and the butterfly effect

We study chaotic dynamics in two-dimensional conformal field theory through out-of-time order thermal correlators of the form 〈W (t)VW (t)V 〉. We reproduce bulk calculations similar to those of [1], by studying the large c Virasoro identity block. The contribution of this block to the above correlation function begins to decrease exponentially after a delay of ∼ t∗− β 2π log β EwEv, where t∗ is the scrambling time β 2π log c, and Ew, Ev are the energy scales of the W,V operators. ar X iv :1 41 2. 51 23 v2 [ he pth ] 4 F eb 2 01 5

[1]  Marina Schroder,et al.  Pct Spin And Statistics And All That , 2016 .

[2]  H. Verlinde,et al.  Conformal bootstrap, universality and gravitational scattering , 2014, 1412.5205.

[3]  Daniel A. Roberts,et al.  Localized shocks , 2014, 1409.8180.

[4]  S. Shenker,et al.  Stringy effects in scrambling , 2014, 1412.6087.

[5]  Leonard Susskind,et al.  Entanglement is not enough , 2014, 1411.0690.

[6]  T. Takayanagi,et al.  Quantum entanglement of localized excited states at finite temperature , 2014, Journal of High Energy Physics.

[7]  Thomas Hartman,et al.  Holographic entanglement entropy from 2d CFT: heavy states and local quenches , 2014, 1410.1392.

[8]  L. Susskind,et al.  Switchbacks and the Bridge to Nowhere , 2014, 1408.2823.

[9]  L. Susskind,et al.  Complexity and Shock Wave Geometries , 2014, 1406.2678.

[10]  Stefan Leichenauer.  Disrupting Entanglement of Black Holes , 2014, 1405.7365.

[11]  J. Kaplan,et al.  Universality of long-distance AdS physics from the CFT bootstrap , 2014, 1403.6829.

[12]  L. Susskind.  Addendum to computational complexity and black hole horizons , 2014, 1403.5695.

[13]  L. Susskind.  Computational complexity and black hole horizons , 2014, 1402.5674.

[14]  S. Shenker,et al.  Multiple shocks , 2013, 1312.3296.

[15]  S. Shenker,et al.  Black holes and the butterfly effect , 2013, Journal of High Energy Physics.

[16]  Thomas Hartman.  Entanglement Entropy at Large Central Charge , 2013, 1303.6955.

[17]  J. Maldacena,et al.  Time evolution of entanglement entropy from black hole interiors , 2013, 1303.1080.

[18]  P. Hayden,et al.  Towards the fast scrambling conjecture , 2011, Journal of High Energy Physics.

[19]  Omar Fawzi,et al.  Scrambling speed of random quantum circuits , 2012, 1210.6644.

[20]  L. Susskind,et al.  Fast Scram blers , 2008, 0808.2096.

[21]  P. Hayden,et al.  Black holes as mirrors: Quantum information in random subsystems , 2007, 0708.4025.

[22]  J. Penedones,et al.  Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion , 2007, 0707.0120.

[23]  J. Penedones,et al.  Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions , 2006, hep-th/0611123.

[24]  J. Penedones,et al.  Eikonal approximation in AdS/CFT: from shock waves to four-point functions , 2006, hep-th/0611122.

[25]  H. Osborn,et al.  Conformal four point functions and the operator product expansion , 2000, hep-th/0011040.

[26]  G. Horowitz,et al.  Black holes, shock waves, and causality in the AdS/CFT correspondence , 1999, hep-th/9901012.

[27]  Alexander M. Polyakov,et al.  Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory , 1996 .

[28]  Paul Ginsparg,et al.  Applied Conformal Field Theory , 1988, hep-th/9108028.

[29]  M. Mattis.  Correlations in 2-dimensional critical theories , 1987 .

[30]  G. Hooft,et al.  The gravitational shock wave of a massless particle , 1985 .

[31]  A. Larkin,et al.  Quasiclassical Method in the Theory of Superconductivity , 1969 .