Complexity of formation in holography

A bstract It was recently conjectured that the quantum complexity of a holographic boundary state can be computed by evaluating the gravitational action on a bulk region known as the Wheeler-DeWitt patch. We apply this complexity=action duality to evaluate the ‘complexity of formation’ [1, 2], i.e....

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Bibliographic Details
Published in:The journal of high energy physics Vol. 2017; no. 1; pp. 1 - 61
Main Authors: Chapman, Shira, Marrochio, Hugo, Myers, Robert C.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2017
Springer Nature B.V
Subjects:
Boundaries
Classical and Quantum Gravitation
Complexity
Computation
Elementary Particles
Entropy
Formations
Gravitation
High energy physics
Holography
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
AdS-CFT Correspondence
Black Holes
ISSN:1029-8479, 1029-8479
Online Access:Get full text
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Summary:A bstract It was recently conjectured that the quantum complexity of a holographic boundary state can be computed by evaluating the gravitational action on a bulk region known as the Wheeler-DeWitt patch. We apply this complexity=action duality to evaluate the ‘complexity of formation’ [1, 2], i.e. the additional complexity arising in preparing the entangled thermofield double state with two copies of the boundary CFT compared to preparing the individual vacuum states of the two copies. We find that for boundary dimensions d > 2, the difference in the complexities grows linearly with the thermal entropy at high temperatures. For the special case d = 2, the complexity of formation is a fixed constant, independent of the temperature. We compare these results to those found using the complexity=volume duality.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP01(2017)062