Topics in Holography and Four Dimensional Superconformal Field Theories.

[摘要] Strong dynamics in physical systems underpin a plethora of phenomena in nature.However, there had not exist many theoretical tools for probing such systems in quantum field theories until the discovery of supersymmetry and holography.In this thesis, we use these frameworks to study strongly coupled dynamics. In chapters two and three, we compute the entanglement entropy of several field theories at zero and finite temperature by using a holographic proposal.We find that the scaling of the entanglement entropy as a function of the size of the system is different in the various phases of the theory.This indicates that the entanglement entropy can be used to detect phase transitions in field theories.For all the systems we studied, we use the entanglement entropy to characterise the types of transitions present.In chapters four and five, we find consistent truncations of the fermionic sectors of M-theory and IIB superstring theory compactified on Sasaki-Einstein seven and five manifolds, respectively.The goal in these chapters is to provide string theory and M-theory embeddings of phenomenological studies of condensed matter systems in holography.We were unable to find truncations to a single fermion as is required by many models.The truncations also contain new types of couplings that were not studied in the literature.Thus we also provided motivations for new phenomenological models.In chapter six, we develop methods for constructing strongly interacting N=1 superconformal field theories (SCFT) that contain Gaiotto;;s T_N theories.We, then, propose the existence of many new four dimensional SCFT;;s.Finally in chapter seven, we study the low energy dynamics of M5-branes wrapping two dimensional Riemann surfaces inside a Calabi-Yau threefold.By using holography, we argue that the long distance physics is describe by a new class of four dimensional SCFT;;s.We, then, construct a set of supersymmetric field theories whose low energy limit correspond to a large subclass of these SCFT;;s.All of the field theories contain T_N;;s and the constructions use tools developed in chapter six.

[发布机构] University of Michigan

[效力级别] Holography and AdS/CFT

[关键词] String Theory;Holography and AdS/CFT;Superconformal Field Theories;Physics;Science;Physics