# Your search: "author:"Gutperle, Michael""

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## Scholarly Works (17 results)

This dissertation summarizes my research in the Lifshitz higher spin Chern-Simons theory and its relation to the integrable system KdV hierarchy as a Ph.D. candidate at UCLA. In Chapter 1, I briefly review the higher spin gravity theory and introduce the Chern-Simons theory as a realization of the Vasiliev theory in three dimensional spacetime. In Chapter 2, I review the KdV hierarchies. In Chapter 3, I discuss how to construct a solution to the Chern-Simons theory which yields a spacetime that exhibits Lifshitz scaling, I also calculate the boundary charge algebra and show the asymptotic Lifshitz symmetry is realized in terms of it. In Chapter 4, I reveal the relation between the Lifshitz Chern-Simons theory and the KdV hierarchies (in the non-supersymmetric case), a proof of the general correspondence is also given using the Drinfeld-Sokolov formalism. In Chapter 5, I work out the supersymmetric extension of this correspondence in a particular case, with the boundary charge algebra of the supersymmetric Chern-Simons theory and the second Hamiltonian structure of the super KdV identified. In Chapter 6, I discuss on the results of my study and possible directions of future research.

A quantum observable which received renewed attention recently is entanglement entropy. It's application ranges over several fields in physics, from condensed matter physics to general relativity. In this dissertation we study entanglement entropy for quantum field theories in the presence of defects and singularities.

We study entanglement entropy using the framework of AdS/CFT correspondence. We focus on entangling surfaces across ball-shaped regions for systems outside their ground state. Quantum field theories in the presence of defects are considered first. These are the six-dimensional $(2,0)$ theory in the presence of Wilson surfaces and the four-dimensional $\cN = 4$ super-Yang-Mills theory in the presence of surface defects of the disordered type. Their holographic entanglement entropy is calculated applying the Ryu-Takayanagi prescripstion on their holographic duals, which are eleven-dimensional supergravity (M-theory) solutions for the former and ten-dimensional type IIB supergravity solutions for the latter. Other holographic observables are computed as well: the holographic stress tensor and the expectation value of the defect (operator). For the disordered defects, an alternative expression for the additional entanglement entropy due to the defect (in terms of expectation values) is derived, adapting the method of Lewkowycz and Maldacena for Wilson loops. The two entanglement entropies agree up to an additional term, the origin of which may be attributed to the conformal anomaly of even dimensional defects as we discuss.

The holographic entanglement and free energy is computed for five-dimensional super conformal field theories, starting from their holographic supergravity duals. Although the supergravity solutions possess singularities, these do not obstruct our calculations. The expected relation between the two observables is verified. This supports the supergravity solutions as holographic duals and gives the first quantitative results for five-dimensional superconformal field theories.

We study three aspects of gauge-gravity duality. First, we explore holographic models of

conformal field theories with boundary by way of holographic renormalization group flows.

Second, we propose an extension and application of the covariant holographic entangelement

entropy proposal to warped anti-de-Sitter spacetimes. Third, we exhibit the existence of

higher-spin black holes with Lifshitz asymptotics in the Chern-Simons formulation of higher

spin gravity.

We explore interfaces and junctions joining multiple two-dimensional conformal field theories, with the goal of calculating entanglement entropies in their presence and exploring their holographic duals. In chapter 1 we start with an overview of the three subjects, collecting various well-known results and reviewing some foundational works.

In chapter 2 we calculate the holographic entanglement entropy in the presence of a conformal interface for a geometric configuration in which the entangling region lies on one side of the interface. For the supersymmetric Janus solution we find exact agreement between the holographic and conformal field theory calculation of the entanglement entropy.

In chapter 3 we calculate the entanglement entropy for topological interfaces in rational conformal field theories for the case where the interface lies at the boundary of the entangling interval and for the case where it is located in the center of the entangling interval. We compare the results to each other and also to the left/right entropy of a related boundary conformal field theory. We also comment on the entanglement entropies for topological interfaces in Liouville theory.

In chapter 4 we consider entanglement through permeable junctions of N free boson and free fermion conformal field theories. We constrain the form of the general boundary state and calculate the replicated partition functions with interface operators inserted, from which the entanglement entropy is calculated. We find the functional form of the universal and constant terms to be similar to the N=2 case, depending only of the total transmission of the junction and the unit volume of the zero mode lattice. For N>2 we see a subleading divergent term which does not depend on the parameters of the junction. For N=3 we consider some specific geometries and discuss various limits.

In chapter 5 we investigate topological interfaces between three-dimensional Abelian Chern-Simons theories in the context of the AdS_3/CFT_2 correspondence. We show that it is possible to connect the topological interfaces in the bulk Chern-Simons theory to topological interfaces in the dual conformal field theory on the boundary. In addition to the [U(1)]^{2N} Chern-Simons theory on AdS_3, we show that it is possible to find boundary counter terms which lead to the N conserved currents in the dual two-dimensional conformal field theory.