BPS states and their reductions

We develop a method to identify the BPS states in the Hilbert space of a supersymmetric field theory on a generic curved space which preserves at least two real supercharges. We also propose a one-to-one map between BPS states in d-dimensional field theories and states that contribute to the supersymmetric partition function of a corresponding (d-1)-dimensional field theory. As an application we obtain the superconformal index on rounded and squashed three spheres, and we show a natural reduction of the respective indices to the three-dimensional exact partition functions. We discuss the validity of the correspondence both at the perturbative and at the non-perturbative level and exploit the idea to uplift the computation of the exact supersymmetric partition function on a general manifold to a higher dimensional index.Comment: 25 pages, 1 figure, typos fixe

GeorgiosTheotokis&AyselYıldız (eds.),A Military History of the Mediterranean Sea. Aspects of War, Diplomacy and Military Elites, Leiden, Brill, 2018.

Review of the book by GeorgiosTheotokis&AyselYıldız (eds.), A Military History of the Mediterranean Sea. Aspects of War, Diplomacy and Military Elites, Leiden, Brill, 2018, pp. XV+473

Review of Georgios Theotokis & Aysel Yıldız (eds.), A Military History of the Mediterranean Sea. Aspects of War, Diplomacy and Military Elites, Leiden, Brill, 2018, pp. XV+473.

Review of the book by Georgios Theotokis & Aysel Yıldız (eds.), A Military History of the Mediterranean Sea. Aspects of War, Diplomacy and Military Elites, Leiden, Brill, 2018, pp. XV+473

« Demanio » o « feudo » ? L’università della Cava tra la signoria monastica e la corona angioina. Centri, periferia e uffici nel Regno di Napoli (XIII-XV)

Les transformations politiques et sociales, commencées entre la fin du xiiie et le xive siècle ont donné lieu à une combinaison de plusieurs éléments qui se chevauchent, où le territoire et la juridiction coïncident à peine et où toute institution se répand rarement sur une zone contiguë. L’origine de la ville de Cava (royaume de Naples), entre la fin du XIIIe et le milieu du XVe siècle, montre comment les deux entités, royale et monastico-féodale, ont interagi entre elles dans une dialectique spécifique entre les centres – la couronne et le monastère de la Trinité – et la périphérie (l’universitas de Cava). Les privilèges royaux et féodaux sont les objets de cette investigation, qui prend aussi en considération les événements concernant Cava, Salerne et l’abbaye durant cette période.The political and social transformations, started between the end of the XIII and XIV centuries have made a combination of several overlapping layers, where the territory and jurisdiction hardly coincide and where any institution rarely spread over a contiguous area. The origin of the city of Cava (Kingdom of Naples) between the end of the XIII and the middle of XV centuries shows how both characters (royal and monastic-feudal) interacted each other in a specific dialectic between centres – the crown and the monastery of Trinity – and periphery (the universitas of Cava). Royal and feudal privileges are the setting where this investigation works not forgetting what happened concerning Cava, Salerno and the abbey during that period

Infrared stability of ABJ-like theories

We consider marginal deformations of the superconformal ABJM/ABJ models which preserve N=2 supersymmetry. We determine perturbatively the spectrum of fixed points and study their infrared stability. We find a closed line of fixed points which is IR stable. The fixed point corresponding to the ABJM/ABJ models is stable under marginal deformations which respect the original SU(2)xSU(2) invariance, while deformations which break this group destabilize the theory which then flows to a less symmetric fixed point. We discuss the addition of flavor degrees of freedom. We prove that in general a flavor marginal superpotential does not destabilize the system in the IR. An exception is represented by a marginal coupling which mixes matter charged under different gauge sectors. Finally, we consider the case of relevant deformations which should drive the system to a strongly coupled IR fixed point recently investigated in arXiv:0909.2036 [hep-th].Comment: 1+11 pages, 4 figures; v2: minor correction

Metastable Vacua in Superconformal SQCD-like Theories

We study dynamical supersymmetry breaking in vector-like superconformal N=1 gauge theories. We find appropriate deformations of the superpotential to overcome the problem of the instability of the non supersymmetric vacuum. The request for long lifetime translates into constraints on the physical couplings which in this regime can be controlled through efficient RG analysis.Comment: 17 pages, 7 figures, JHEP3.cl

Z-extremization and F-theorem in Chern-Simons matter theories

The three dimensional exact R symmetry of N=2 SCFTs extremizes the partition function localized on a three sphere. Here we verify this statement at weak coupling. We give a detailed analysis for two classes of models. The first one is an SU(N)_k gauge theory at large k with both fundamental and adjoint matter fields, while the second is a flavored version of the ABJ theory, where the CS levels are large but they do not necessarily sum up to zero. We study in both cases superpotential deformations and compute the R charges at different fixed points. When these fixed points are connected by an RG flow we explicitly verify that the free energy decreases at the endpoints of the flow between the fixed points, corroborating the conjecture of an F-theorem in three dimensions.Comment: 28 pages, 3 figures, JHEP.cls, minor corrections, references adde

The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals

We compute the large N limit of the localized three dimensional free energy of various field theories with known proposed AdS duals. We show that vector-like theories agree with the expected supergravity results, and with the conjectured F-theorem. We also check that the large N free energy is preserved by the three dimensional Seiberg duality for general classes of vector like theories. Then we analyze the behavior of the free energy of chiral-like theories by applying a new proposal. The proposal is based on the restoration of a discrete symmetry on the free energy before the extremization. We apply this procedure at strong coupling in some examples and we discuss the results. We conclude the paper by proposing an alternative geometrical expression for the free energy.Comment: 40 pages, 7 figures, using jheppub.sty, references adde