MSc thesis defence Kristian Toccacelo

Title: On the holographic complexity of Janus geometries

Abstract: Relatively recent progress in this field has unveiled remarkable connections between the theory of quantum information and quantum gravity. In fact, in holography the entropy of a spatial subsystem in the boundary CFT is realized through the Ryu-Takayanagi formula. Via this formula we can compute the entropy by computing the area of a codimension-one surface embedded in the bulk spacetime and anchored to the subregion at the boundary. However, another quantum information quantity has attracted attention in the last years: computational complexity. It was first introduced to explain the evolution in time of the Einstein- Rosen bridge, as this growth can’t be accounted for by entanglement entropy since the wormhole keeps on growing long after the thermalization time. Quantum complexity is usually defined in quantum circuits as the minimum number of k−local gates connecting a generic state in the Hilbert space to a reference state in the same Hilbert space. Two proposals have been put forward as to what bulk quantity is dual to the complexity of states in the boundary. The first proposal, known as the CV conjecture (or the complexity=volume conjecture), states that complexity is dual to the maximal volume of a codimension-one sub-manifold attached to the boundary. The other proposal is the so-called CA conjecture (or the complexity=action conjecture), which relates the complexity of states to the bulk action evaluated on a spacetime region known as the Wheeler-de Witt patch, that is, the bulk domain of dependence of a Cauchy surface anchored at the boundary state. In this talk, we investigate the complexity=volume proposal in the case of Janus AdS_3 and Janus AdS_5 geometries. We also study the time evolution of the extremal volume for the time-dependent Janus BTZ black hole. This background is not dual to an interface but to a pair of entangled CFTs with different values of the couplings. We comment on the universality structure of UV divergences and on the time evolution of complexity in the time-dependent scenario.

Only a limited number of people can attend in person in Auditorium A. You can also follow the defence online through the following Zoom link: