Holographic complexity : bulk tests and implications

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].Physic