Holographic Complexity and Spacetime Locality

The work in this thesis provides a connection between the notion of holographic complexity in the form of the so-called Complexity = Volume proposal and the gravitational clumping of matter, within the AdS/CFT correspondence. In this defense, I will present the derivation of the ‘Momentum/Complexity’ (PVC) correspondence of this thesis, which generalizes previous ‘Momentum/Size’ relations in the literature beyond the scrambling time for finite entropy thermal states. The characteristic linear regime of complexity is associated to a frozen radial momentum of the excitation in the black hole interior. I will then discuss the sense in which the PVC correspondence formalizes the recurrent idea that the gravitational clumping of matter increases the complexity of the quantum state, giving a list of properties of the relevant component of the momentum of matter. I will end by using the PVC correspondence to discuss the sensitivity of VC to fast scrambling at early times.

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Marín Sasieta PhD