Entanglement and confinement in QFT and gauge/gravity.

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

Confinement, phase transitions and non-locality in the entanglement entropy

In this paper we study the conjectural relation between confinement in a quantum field theory and the presence of a phase transition in its corresponding entanglement entropy. We determine the sufficient conditions for the latter and compare to the conditions for having a confining Wilson line. We demonstrate the relation in several examples. Superficially, it may seem that certain confining field theories with a non-local high energy behaviour, like the dual of D5 branes wrapping a two-cycle, do not admit the corresponding phase transition. However, upon closer inspection we find that, through the introduction of a regulating UV-cutoff, new eight-surface configurations appear, that satisfy the correct concavity condition and recover the phase transition in the entanglement entropy. We show that a local-UV-completion to the confining non-local theories has a similar effect to that of the aforementioned cutoff.Comment: 64 pages. Lots of figure

Où en est la gauche israélienne ?

Depuis le début de l'existence de l'État d’Israël, le partage droite/gauche a surtout eu tendance à s'enraciner autour de la question du sionisme et de l’attitude observée à l’égard de la question palestinienne, ce qui explique pourquoi les questions sociales peuvent apparaître comme secondaires pour définir la gauche israélienne. Il existe donc une gauche antisioniste et une gauche sioniste ou post-sioniste. Leurs attitudes à l’égard du conflit israélo-arabe, de la minorité arabe israélienne et des critères d’identité israéliens sont différents même si l ’émergence d 'un courant pacifiste a tendance à gommer quelque peu les divergences initiales. Aujourd’hui, une recomposition de la gauche semble se produire. En plus des partis de gauche, des mouvements associatifs, pacifiste, féminins, juifs orientaux, participent à l’émergence déformés nouvelles au sein des gauches israéliennes.Warschawski Michael. Où en est la gauche israélienne ?. In: Recherches Internationales, n°54, 1998. pp. 9-20

Les révoltes arabes vues d’Israël

Les «printemps arabes» ont principalement profité à la mouvance des Frères musulmans qui se retrouvent au pouvoir en Tunisie et en Égypte. Washington a fait le choix d’accompagner le mouvement. La position israélienne se trouve aujourd’hui d’autant plus fragilisée que la réélection d’Obama s’est réalisée malgré tous les efforts mis en oeuvre par Tel-Aviv pour la contrarier. Israël va devoir compter avec une Égypte plus solidaire des Palestiniens et décidée à mettre en oeuvre une diplomatie plus active.Warschawski Michael. Les révoltes arabes vues d’Israël. In: Recherches Internationales, n°94, 2013. Temps couvert pour les printemps arabes. pp. 83-92

État, nation et nationalisme : Actualité du sionisme

Michel Warschawski, State, Nation and Nationalism. Zionism Today The debate over Zionism today is not theoretical or simply over semantics. It has direct implications on Israeli policies and on the meanings of the Oslo peace agreement. The Oslo declaration is in fact the most striking victory of Zionism because it allows continued Israeli control over the occupied territories as well as the continuation of Israeli settlement activity in them. At the same time it contributes to a separation of the two communities that is not imposed upon the Palestinians, but rather accepted by the Palestinian National Authority as an element of the liberation and of national sovereignty.Warchawski Michel. État, nation et nationalisme : Actualité du sionisme. In: L'Homme et la société, N. 114, 1994. État démocratique ou état confessionnel ? Autour du conflit israël-palestine. pp. 27-36

Le dernier des Titans. Réflexions sur Yeshayahou Leibowitz, 1903-1994

Warschawski Michael, Beaurain Nicole, Portis Larry. Le dernier des Titans. Réflexions sur Yeshayahou Leibowitz, 1903-1994. In: L'Homme et la société, N. 114, 1994. État démocratique ou état confessionnel ? Autour du conflit israël-palestine. pp. 134-137