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Addison-Wesley Publishing Company, Massachusetts, 1976
L. A. Santaló, Integral Geometry and Geometric Probability · 1976
Earlier work this paper cites.
M. Banados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time , Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
Addison-Wesley, Reading, Massachusetts, 1994
C. M. Papadimitriou, Computational complexity · 1994
Earlier work this paper cites.
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity , Int. J. Theor. Phys. 38
1999
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT , Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
M. A. Nielsen, A geometric approach to quantum circuit lower bounds , Quantum Information and Computation 6
2006
Earlier work this paper cites.
P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory , J. Phys. A42
Original
2009
Earlier work this paper cites.
M. Van Raamsdonk, Building up spacetime with quantum entanglement , Gen. Rel. Grav. 42
Original
2010
Earlier work this paper cites.
G. Evenbly and G. Vidal, Tensor network states and geometry , Journal of Statistical Physics 145
2011
Earlier work this paper cites.
B. Swingle, Entanglement Renormalization and Holography , Phys. Rev. D86
Original
2012
Earlier work this paper cites.
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries , Phys. Rev. D90
Original
2014
Earlier work this paper cites.

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2017

Topological Complexity in AdS3/CFT2

Abt, Raimond, Erdmenger, Johanna, Hinrichsen, Haye et al.

Understand

We consider subregion complexity within the AdS3/CFT2 correspondence.

We rewrite the volume proposal, according to which the complexity of a reduced density matrix is given by the spacetime volume contained inside the associated Ryu-Takayanagi (RT) surface, in terms of an integral over the curvature.
Using the Gauss-Bonnet theorem we evaluate this quantity for general entangling regions and temperature.
In particular, we find that the discontinuity that occurs under a change in the RT surface is given by a fixed topological contribution, independent of the temperature or details of the entangling region.

Built on

Addison-Wesley Publishing Company, Massachusetts, 1976
L. A. Santaló, Integral Geometry and Geometric Probability · 1976
Earlier work this paper cites.
M. Banados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time , Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
Addison-Wesley, Reading, Massachusetts, 1994
C. M. Papadimitriou, Computational complexity · 1994
Earlier work this paper cites.
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity , Int. J. Theor. Phys. 38
1999
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT , Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
M. A. Nielsen, A geometric approach to quantum circuit lower bounds , Quantum Information and Computation 6
2006
Earlier work this paper cites.
P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory , J. Phys. A42
Original
2009
Earlier work this paper cites.
M. Van Raamsdonk, Building up spacetime with quantum entanglement , Gen. Rel. Grav. 42
Original
2010
Earlier work this paper cites.
G. Evenbly and G. Vidal, Tensor network states and geometry , Journal of Statistical Physics 145
2011
Earlier work this paper cites.
B. Swingle, Entanglement Renormalization and Holography , Phys. Rev. D86
Original
2012
Earlier work this paper cites.
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries , Phys. Rev. D90
Original
2014
Earlier work this paper cites.