First Law of Holographic Complexity

First Law of Holographic Complexity

We investigate the variation of holographic complexity for two nearby target states. Based on Nielsen's geometric approach, we find the variation only depends on the end point of the optimal trajectory, a result which we designate the first law of complexity. As an example, we examine the compl...

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Veröffentlicht in:Physical review letters 2019-08, Vol.123 (8), p.081601-081601, Article 081601
Hauptverfasser: Bernamonti, Alice, Galli, Federico, Hernandez, Juan, Myers, Robert C, Ruan, Shan-Ming, Simón, Joan
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Complexity
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container_issue 8
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container_title Physical review letters
container_volume 123
creator Bernamonti, Alice
Galli, Federico
Hernandez, Juan
Myers, Robert C
Ruan, Shan-Ming
Simón, Joan
description We investigate the variation of holographic complexity for two nearby target states. Based on Nielsen's geometric approach, we find the variation only depends on the end point of the optimal trajectory, a result which we designate the first law of complexity. As an example, we examine the complexity=action conjecture when the anti-de Sitter vacuum is perturbed by a scalar field excitation, which corresponds to a coherent state. Remarkably, the gravitational contributions completely cancel and the final variation reduces to a boundary term coming entirely from the scalar field action. Hence, the null boundary of Wheeler-DeWitt patch appears to act like the "end of the quantum circuit".
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title First Law of Holographic Complexity
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