Topics in quantum field theory and holography

Quantum Field Theory;Holography

Parrikar, Onkar

关键词: Quantum Field Theory;    Holography;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/92702/PARRIKAR-DISSERTATION-2016.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

In the first part of this thesis, we will study free fermions as models for topological insulators, on gravitational backgrounds which include both torsion and curvature, in d = 2 + 1 and d = 4 + 1 dimensions. We compute the parity-odd effective actions for these systems, and use these effective actions to deduce the structure of anomalies (in particular, the torsional contributions) in the edge states which live on the boundary between two different bulk phases. We also give intrinsic, microscopic derivations of these torsional anomalies by considering Hamiltonian spectral flow for edge states in the presence of torsion. All of these calculations fit perfectly within the well-known framework of anomaly inflow, and extend the framework to include torsional contributions. Furthermore, our condensed-matter-inspired setup provides natural resolutions to some previously ill-understood ultraviolet divergences in intrinsic edge calculations of torsional anomalies.In the second part of this thesis, we consider the Bosonic and Fermionic U(N) vector models close to their free fixed points, with single-trace deformations turned on. We derive the higher-spin holographic duals corresponding to these vector models by first formulating these theories in terms of the geometry of infinite jet bundles, and then interpreting the renormalization group equations for single-trace deformations as Hamilton's equations of motion on a one-higher dimensional emergent spacetime. We evaluate the resulting bulk on-shell action explicitly, and show that it reproduces all the correlation functions of the vector models. Furthermore, we show that the linearized bulk equations of motion contain the Fronsdal equations of motion on Anti-de Sitter space, thus proving equivalence with Vasiliev higher-spin theories to linearized order. The bulk theory we derive is consistent with the known AdS/CFT framework, and gives a concrete boundary to bulk implementation of AdS/CFT as a geometrization of the renormalization group.