Complexity of Holographic Flavours and causality in QFTs with Gauss-Bonnet dual - GARCIA ABAD, FRANCISCO JOSE (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)
This thesis is the compilation of two different projects undertaken during my PhD programme. Chapter 2 covers the work on quantum complexity. Quantum complexity of a thermofield double state in a strongly coupled quantum field theory has been argued to be holographically related to the action evaluated on the Wheeler-DeWitt patch. The growth rate of quantum complexity in systems dual to Einstein-Hilbert gravity saturates a bound which follows from the Heisenberg uncertainty principle. This work, considers corrections to the growth rate in models with flavor degrees of freedom. These are realized by adding a small number of flavor branes to the system. Holographically, such corrections come from the DBI action of the flavor branes evaluated on the Wheeler-DeWitt patch. After relating corrections to the growth of quantum complexity to corrections to the mass of the system, it is observed that the bound on the growth rate is never violated. Chapter 3 covers the still ongoing project of causality in RG flows of systems with a Gauss-Bonnet gravity holographic dual. In order for the dual field theory to have no causality problems the speed of gravitons near the boundary of AdS must be bounded above by the speed of light. This bound is checked along the RG flow for QFTs that have AdS Gauss-Bonnet spacetime duals. It is found that, for certain values of the Gauss-Bonnet parameter, the field theory becomes acausal when sufficiently far away from the UV.
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Keywords: Quantum Field Theory; Holography; General Relativity