Investigations of Holographic Duality in Two Dimensions

Abstract

This dissertation explores various structural, geometric, statistical and information-theoretic aspects of models of lower-dimensional holography. Chapter 2 is based on work with Ho Tat Lam, Gustavo J. Turiaci and Herman Verlinde [1]. It explores a class of partially entangled thermal states in the Sachdev-Ye-Kitaev model that interpolates between the thermo-field double state and a pure (product) state. We argue that the holographic dual of this class of states consists of two black holes with their interior regions connected via a domain wall, described by the worldline of a massive particle. We compute the size of the interior region and the entanglement entropy as a function of the temperature of each black hole. We argue that the one-sided bulk reconstruction can access the interior region of the black hole. Chapter 3 is based on work with Luca Iliesiu, Jorrit Kruthoff and Zhenbin Yang [2]. It explores a systematic classification of the possible boundary conditions in Jackiw-Teitelboim gravity and discusses their exact quantization. Each boundary condition that we study will reveal new features in JT gravity related to its matrix integral interpretation, its factorization properties, ensemble averaging interpretation, the definition of the theory at finite cutoff, its relation to the physics of near-extremal black holes and its role as a two-dimensional model of cosmology. Chapter 4 is based partly on [3] and on discussions with Ping Gao, Vladimir Narovlansky and Herman Verlinde. We survey several strategies to explore the UV physics of SYK. We provide a Lorentzian Liouville quantum gravity perspective on the double-scaled model. We then describe the construction of a matrix version of SYK within the framework of minimal string theory.