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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Vydáno v:	The journal of high energy physics Ročník 2017; číslo 1; s. 1 - 61
Hlavní autoři:	Chapman, Shira, Marrochio, Hugo, Myers, Robert C.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2017 Springer Nature B.V
Témata:	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
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Abstract	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.
AbstractList	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. 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. Abstract 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.
ArticleNumber	62
Author	Chapman, Shira Myers, Robert C. Marrochio, Hugo
Author_xml	– sequence: 1 givenname: Shira surname: Chapman fullname: Chapman, Shira email: schapman@perimeterinstitute.ca organization: Perimeter Institute for Theoretical Physics – sequence: 2 givenname: Hugo surname: Marrochio fullname: Marrochio, Hugo organization: Perimeter Institute for Theoretical Physics, Department of Physics & Astronomy and Guelph-Waterloo Physics Institute, University of Waterloo – sequence: 3 givenname: Robert C. surname: Myers fullname: Myers, Robert C. organization: Perimeter Institute for Theoretical Physics
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Snippet	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... Abstract It was recently conjectured that the quantum complexity of a holographic boundary state can be computed by evaluating the gravitational action on a... 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...
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SubjectTerms	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
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Title	Complexity of formation in holography
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