The First Law of Complexity

27 Feb 2020  ·  Bernamonti Alice, Galli Federico, Hernandez Juan, Myers Robert C., Ruan Shan-Ming, Simón Joan ·

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 AdS 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". read more

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High Energy Physics - Theory Quantum Physics