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Complexity & Wormholes in Holography

2024
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Release : 2024
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Book Synopsis Complexity & Wormholes in Holography by : Ramesh Chandra Ammanamanchi

Download or read book Complexity & Wormholes in Holography written by Ramesh Chandra Ammanamanchi. This book was released on 2024. Available in PDF, EPUB and Kindle. Book excerpt: "Holography has proven to be a highly successful approach in studying quantum gravity, where a non-gravitational quantum field theory is dual to a quantum gravity theory in one higher dimension. This doctoral thesis delves into two key aspects within the context of holography: complexity and wormholes. In Part I of the thesis, the focus is on holographic complexity. Beginning with a brief review of quantum complexity and its significance in holography, the subsequent two chapters proceed to explore this topic in detail. We study several proposals to quantify the costs of holographic path integrals. We then show how such costs can be optimized and match them to bulk complexity proposals already existing in the literature. In Part II of the thesis, we shift our attention to the study of spacetime wormholes in AdS/CFT. These are bulk spacetime geometries having two or more disconnected boundaries. In recent years, such wormholes have received a lot of attention as they lead to interesting implications and raise important puzzles. We study the construction of several simple examples of such wormholes in general dimensions in the presence of a bulk scalar field and explore their implications in the boundary theory."--

Chaos, Wormholes, and Holography

2023
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Release : 2023
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Book Rating : 755/5 ( reviews)

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Book Synopsis Chaos, Wormholes, and Holography by : Jeremy van der Heijden

Download or read book Chaos, Wormholes, and Holography written by Jeremy van der Heijden. This book was released on 2023. Available in PDF, EPUB and Kindle. Book excerpt: "Combining quantum mechanics and general relativity is one of the most important open problems in theoretical physics. A formal approach towards quantizing gravity is given by the gravitational path integral. However, dealing with quantum fluctuations of spacetime itself is in general a very complicated task. In this thesis, I therefore study a simple model of two-dimensional gravity in Anti-de Sitter (AdS) space where it is possible to calculate exactly a class of such quantum fluctuations, so-called Euclidean wormholes, which correspond to geometries with a non-trivial topology. This computation relies on the holographic principle: the idea that AdS gravity is dual to some microscopic quantum theory without gravity, a conformal field theory (CFT), that lives in one dimension less. Surprisingly, the non-trivial surfaces appear to contain important information about this underlying quantum theory: They point to a deep connection between quantum gravity and quantum chaos. To be precise, the results of this thesis show that black holes in two-dimensional AdS space obey the rules of quantum chaos, and that the relevant quantum effects can be realized geometrically in the path integral. This is an important step towards understanding the quantum nature of black holes. Finally, I study the role of geometric phases in the AdS/CFT correspondence, and show that the modular Berry phase in the CFT is holographically dual to a particular geometric quantity in the AdS space, the so-called bulk symplectic form."--

Studies of Traversable Wormholes and Holography

2022
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Release : 2022
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Book Synopsis Studies of Traversable Wormholes and Holography by : Anderson Seigo Waki Misobuchi

Download or read book Studies of Traversable Wormholes and Holography written by Anderson Seigo Waki Misobuchi. This book was released on 2022. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is based on studies of traversable wormholes within the context of the holographic duality. First, we study the traversability obtained via the introduction of a direct coupling between the two asymptotic boundaries of a non-traversable wormhole and we construct a traversable wormhole with angular momentum. We discuss its dual interpretation and the implications to the information transfer. Second, we study the relation between the Sachdev-Ye-Kitaev (SYK) model and an eternal traversable wormhole with global a AdS2 geometry. We consider a sparse version of the SYK model defined via a regular hypergraph and we numerically simulate a system of two copies of the sparse SYK coupled by a bilinear interaction. We discuss the finite-size effects in this system and obtain the optimal level of sparseness that preserves features of the original SYK model such that it can still be holographically interpreted as a traversable wormhole

Wormholes in Holography

2022
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Release : 2022
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Book Synopsis Wormholes in Holography by : Antonio F. Rotundo

Download or read book Wormholes in Holography written by Antonio F. Rotundo. This book was released on 2022. Available in PDF, EPUB and Kindle. Book excerpt:

Studies in Holographic Complexity

2021
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Release : 2021
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Book Synopsis Studies in Holographic Complexity by : Josiah D. Couch

Download or read book Studies in Holographic Complexity written by Josiah D. Couch. This book was released on 2021. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation will present the work I have done on the conjectured relationship between various bulk quantities designed to capture the growth of the wormhole in eternal black hole spacetimes and the circuit complexity of the boundary state within the context of the AdS/CFT correspondence, i.e., on the topic of ’holographic complexity.’ Four papers are presented here, each focused on the bulk side of this proposed relationship. In these papers, my various co-authors and I seek to improve our understanding of the bulk quantities in question (action of a causal diamond, maximal volume) and test the internal consistency of these proposals and their consistency with our intuition and understanding of the boundary field theory. In particular, the first of these papers focuses on properties of maximal volume slices in black hole spacetimes, along with consequences for the ’complexity = volume’ conjecture. The next paper considers whether ’complexity = action’ is consistent with the intuition we develop about the time evolution of the boundary circuit complexity in space-times dual to non-commutative field theories. The third paper deals with a possible relationship between the rate of increase of complexity and the thermodynamic volume of black hole spacetimes. Finally, the last paper deals with restrictions of the ’complexity = action’ and ’complexity = volume’ conjectures to boundary subregions and their corresponding entanglement wedges and seeks to test the consistency of a conjecture relating these restrictions to the purification complexity of the reduced density matrix

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