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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

Holographic Complexity

2021
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Release : 2021
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Book Synopsis Holographic Complexity by : Stefan Vincent Eccles

Download or read book Holographic Complexity written by Stefan Vincent Eccles. This book was released on 2021. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of four chapters. The first broadly and briefly orients the reader through an introduction to holographic complexity within the AdS/CFT correspondence. The next three chapters correspond to distinct lines of research conducted during my time as a graduate student, chosen for their thematic relation to holographic complexity, and particularly the two conjectures known as "complexity equals volume" (CV), and "complexity equals action" (CA). Chapter two is based on work conducted with Josiah Couch, Willy Fischler, and Ming-Lei Xiao, studying the holographic complexity of noncommutative field theories under the CA conjecture [1]. Chapter three is based on work with Josiah Couch, Phuc Nguyen, and Ted Jacobson, studying general aspects of the CV conjecture, and addressing certain challenges to that proposal [2]. Chapter four is based on work with Elena Caceres, Josiah Couch, and Willy Fischler, testing proposed extensions of both CA and CV that apply them to subsystem complexity [3]

Three Lectures on Complexity and Black Holes

2020-05-11 Science
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Release : 2020-05-11
Genre : Science
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Book Rating : 097/5 ( reviews)

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Book Synopsis Three Lectures on Complexity and Black Holes by : Leonard Susskind

Download or read book Three Lectures on Complexity and Black Holes written by Leonard Susskind. This book was released on 2020-05-11. Available in PDF, EPUB and Kindle. Book excerpt: These three lectures cover a certain aspect of complexity and black holes, namely the relation to the second law of thermodynamics. The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. Lecture two reviews the connection between the second law of complexity and the interior of black holes. Prof. L. Susskind discusses how firewalls are related to periods of non-increasing complexity which typically only occur after an exponentially long time. The final lecture is about the thermodynamics of complexity, and “uncomplexity” as a resource for doing computational work. The author explains the remarkable power of “one clean qubit,” in both computational terms and in space-time terms. This book is intended for graduate students and researchers who want to take the first steps towards the mysteries of black holes and their complexity.

The Ambient Metric

2011-11-14 Mathematics
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Release : 2011-11-14
Genre : Mathematics
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Book Rating : 589/5 ( reviews)

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Book Synopsis The Ambient Metric by : Charles Fefferman

Download or read book The Ambient Metric written by Charles Fefferman. This book was released on 2011-11-14. Available in PDF, EPUB and Kindle. Book excerpt: This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincaré metrics in four dimensions are considered as a special case, leading to a formal power series proof of LeBrun's collar neighborhood theorem proved originally using twistor methods. Conformal curvature tensors are introduced and their fundamental properties are established. A jet isomorphism theorem is established for conformal geometry, resulting in a representation of the space of jets of conformal structures at a point in terms of conformal curvature tensors. The book concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature, applying results in parabolic invariant theory.

Advanced Lectures on General Relativity

2019-01-31 Science
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Release : 2019-01-31
Genre : Science
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Book Rating : 60X/5 ( reviews)

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Book Synopsis Advanced Lectures on General Relativity by : Geoffrey Compère

Download or read book Advanced Lectures on General Relativity written by Geoffrey Compère. This book was released on 2019-01-31. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The four topics covered are: Surface charges as conserved quantities in theories of gravity; Classical and holographic features of three-dimensional Einstein gravity; Asymptotically flat spacetimes in four dimensions: BMS group and memory effects; The Kerr black hole: properties at extremality and quasi-normal mode ringing. Each topic starts with historical foundations and points to a few modern research directions.

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