Browsing by Subject "Holographic complexity"

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Holographic complexity : bulk tests and implications
(2021-05-06) Eccles, Stefan Vincent; Fischler, Willy; Caceres, Elena; Kilic, Can; Paban, Sonia; Shapiro, Paul
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].
Studies in holographic complexity
(2021-05-06) Couch, Josiah D.; Fischler, Willy; Aaronson, Scott; Distler, Jacques; Kilic, Can; Paban, Sonia
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