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Title: Entanglement and confinement in QFT and gauge/gravity
Author: Warschawski, Michael
ISNI:       0000 0004 7425 5014
Awarding Body: Swansea University
Current Institution: Swansea University
Date of Award: 2015
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In this thesis our investigation will follow two branches. We will study Entanglement Entropy in Quantum Field Theories and we will study confinement in Holographic Field Theories. In the study of confinement we will mainly focus on field theories dual to a class of backgrounds in Type IIB supergravity, that is obtained by wrapping D5 branes on a two-cycle on the tip of the conifold. We start by calculating the Entanglement Entropy for a Hilbert Space with a split in field theory degrees of freedom. We apply this novel approach first on a Quantum Field Theory with a light and a heavy scalar and a cubic interaction vertex. We observe divergences in the Entanglement Entropy where the field theory is unstable to decay. We then calculate the Entanglement Entropy for the photon in Quantum Electrodynamics. While the entropy does require a UV-cutoff to remain finite, it is free of singularities. Then, we move on to the study of Entanglement Entropy in the context of the Gauge/Gravity Correspondence. We establish a connection between the existence of a first-order phase transition in Holographic Entanglement Entropy and confinement of the dual field theory. We notice that non-localities in the UV of the confining field theory can m ask the phase transition. We show two methods to resolve this discrepancy. First, we show how novel configurations that show Volume Law divergences rather than the typical Area law divergences, recover the phase transition. Second, we show how a suitable UV completion removing the nonlocalities also leads to discovery. We then provide a Taxonomy of behaviours of the Entanglement Entropy in different confining backgrounds and hint at Invariances of Holographic Entanglement Entropy Third, we study the Wilson Loop for the confining field theories dual to D5 on S 2. We notice, that the Wilson Loop also admits phase transitions. We interpret the reason why these phase transitions occur and test our assumptions by creating background with multiple phase transitions. Last, we notice the mathematical similarity between Holographic Entanglement Entropy and the Wilson Loop. We establish and com pare the conditions on both quantities to probe confinement. We test these conditions on a selection of backgrounds. While also note the source for the difference in their behaviour and establish the precise term responsible. We conclude by analysing whether it m ight be possible at all to find backgrounds that have the exact same qualitative behaviour of the Wilson Loop and the Entanglement Entropy.
Supervisor: Hollowood, Timothy J. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available