RG flows with supersymmetry enhancement and geometric engineering

In this paper we study a class of $\mathcal{N}=2$ SCFTs with ADE global symmetry defined via Type IIB compactification on a class of hypersurfaces in $\mathbb{C}^3\times\mathbb{C}^*$. These can also be constructed by compactifying the 6d (2,0) theory of type ADE on a sphere with an irregular and a full punctures. When we couple to the ADE moment map a chiral multiplet in the adjoint representation and turn on a (principal) nilpotent vev for it, all the theories in this family display enhancement of supersymmetry in the infrared. We observe that all known examples of lagrangian theories which flow, upon the same type of deformation, to strongly coupled $\mathcal{N}=2$ theories fit naturally in our framework, thus providing a new perspective on this topic. We propose an infrared equivalence between this RG flow and a manifestly $\mathcal{N}=2$ preserving one and, as a byproduct, we extract a precise prescription to relate the SW curves describing the UV and IR fixed points for all theories with A or D global symmetry. We also find, for a certain subclass, a simple relation between UV and IR theories at the level of chiral algebras.Comment: clarifications added, version published in JHE

Infrared enhancement of supersymmetry in four dimensions

We study a recently-found class of RG flows in four dimensions exhibiting enhancement of supersymmetry in the infrared, which provides a lagrangian description of several strongly-coupled N=2 SCFTs. The procedure involves starting from a N=2 SCFT, coupling a chiral multiplet in the adjoint representation of the global symmetry to the moment map of the SCFT and turning on a nilpotent expectation value for this chiral. In this note we show that, combining considerations based on 't Hooft anomaly matching and basic results about the N=2 superconformal algebra, it is possible to understand in detail the mechanism underlying this phenomenon and formulate a simple criterion for supersymmetry enhancement which allows us to bypass the analysis with a-maximization. As a byproduct, we propose an algorithm to identify a lagrangian UV completion of a given N=2 SCFT under an RG flow of this type, provided there is one.Comment: 24 pages, references adde

Four dimensional superconformal theories from M5 branes

We study N=1 superconformal theories in four dimensions obtained wrapping M5 branes on a Riemann surface. We propose a method to determine from the spectral curve the scaling dimension of chiral operators in the SCFT. Whenever the R-symmetry has to be determined via a-maximization, our procedure allows us to determine the charge of chiral operators under the "trial" R-symmetry. Our proposal reduces to the correct prescription in the special case of N=2 theories of class S. We perform several consistency checks and apply our method to study some new SCFT's such as N=1 deformations of Argyres-Douglas theories.Comment: 29 pages, 6 figures. References and clarifications added. Version published in JHE

N=1\mathcal{N} = 1 superconformal theories with DND_N blocks

We study the chiral ring of four-dimensional superconformal field theories obtained by wrapping M5-branes on a complex curve inside a Calabi-Yau three-fold. We propose a field theoretic construction of all the theories found by Bah, Beem, Bobev and Wecht by introducing new building blocks, and prove several $\mathcal{N} = 1$ dualities featuring the latter. We match the central charges with those computed from the M5-brane anomaly polynomial, perform the counting of relevant operators and analyze unitarity bound violations. As a byproduct, we compute the exact dimension of "heavy operators" obtained by wrapping an M2-brane on the complex curve.Comment: 45 pages, 17 figures; v2: typos fixed, minor changes, references added, conclusions added, version published in Phys. Rev.

Dualities for adjoint SQCD in three dimensions and emergent symmetries

In this paper we study dualities for $\mathcal{N}=2$ gauge theories in three dimensions with matter in the fundamental and adjoint representation. The duality we propose, analogous to mirror symmetry, is obtained starting from $\mathcal{N}=4$ mirror theories and turning on a certain superpotential deformation involving monopole operators. We study the role of emergent symmetries in the dual theory, focusing on the case of models with gauge symmetry $U(2)$ or $SU(2)$. We find that $SU(2)$ adjoint SQCD with one flavor and zero superpotential is dual to SQED with two flavors and three singlets. As a byproduct, we recover several dualities for theories with $\mathcal{N}=2$ and $\mathcal{N}=4$ supersymmetry, including the duality appetizer of Jafferis and Yin.Comment: 30 pages, 10 figures; references adde

Confinement and duality in supersymmetric gauge theories

In this thesis we review the Seiberg-Witten solution of four dimensional N=2 gauge theories, the six-dimensional construction of these models recently proposed by Gaiotto and the BPS quiver technique for the determination of the BPS spectrum of N=2 theories. We then study how these recent developments allow to better understand nonperturbative aspects such as confinement and dynamical symmetry breaking in the N=1 theories obtained starting from N=2 SQCD and adding a mass term for the chiral multiplet in the adjoint of the gauge group. We find an unusual realization of the 't Hooft-Mandelstam mechanism, in which confinement and dynamical symmetry breaking are due to the condensation of different degrees of freedom.Comment: PhD thesis (Advisor: Kenichi Konishi). 196 pages, 15 figure

T-branes through 3d mirror symmetry

T-branes are exotic bound states of D-branes, characterized by mutually non-commuting vacuum expectation values for the worldvolume scalars. The M/F-theory geometry lifting D6/D7-brane configurations is blind to the T-brane data. In this paper, we make this data manifest, by probing the geometry with an M2-brane. We find that the effect of a T-brane is to deform the membrane worldvolume superpotential with monopole operators, which partially break the three-dimensional flavor symmetry, and reduce supersymmetry from N=4 to N=2. Our main tool is 3d mirror symmetry. Through this language, a very concrete framework is developed for understanding T-branes in M-theory. This leads us to uncover a new class of N=2 quiver gauge theories, whose Higgs branches mimic those of membranes at ADE singularities, but whose Coulomb branches differ from their N=4 counterparts.Comment: 36 page

I pazienti con Sindrome di DiGeorge e delezione di Crkl mostrano una sbilanciata risposta proliferativa legata alla riduzione del fattore trascrizionale c-Fos

2012/2013La sindrome di DiGeorge (o del22q11.2) è una immunodeficienza primitiva, avente una incidenza di 1 / 5000 nati vivi. Essa è causata da una delezione, in eterozigosi, di un tratto del braccio lungo del cromosoma 22, di circa 3 MB. La sindrome si accompagna a malformazioni cardiache e del tronco aortico, oltre che ad anomalie del volto e dell’arco palatino, con ipoplasia/aplasia del timo e delle paratiroidi. Oltre alle patologie cardiache gli individui affetti soffrono di tetania e convulsioni, dismorfismi facciali e immunodeficienze con infezioni ripetute sia batteriche che virali, in particolare alle vie aeree sia alte che basse. Spesso sono frequenti episodi di autoimmunità. In generale la sindrome mostra una ampia variabilità fenotipica, anche fra individui della stessa famiglia. Le basi delle alterazioni immunologiche di questa sindrome non sono ancora pienamente comprese e restano anzi assai vaghe. Fra le proteine delete vi è la proteina Crkl, una proteina appartenente alla più ampia famiglia degli adattatori Crk. Crkl prende parte ad importanti processi biologici quali chemotassi, adesione, apoptosi e proliferazione. Crkl è una proteina coinvolta infatti nel signaling di svariati fattori di crescita e citochine come SDF-1α, interferoni di tipo I, GM-CSF ed IL-2. Il nostro scopo è stato quello di comprendere se le alterazioni funzionali dei linfociti T, osservabili in questa sindrome, siano correlabili alla aplo-insufficienza di Crkl. Noi abbiamo analizzato, in un gruppo di pazienti affetti da del22q11.2 la proliferazione, l’apoptosi e l’espressione di vari markers di attivazione, nei linfociti T dopo stimolazione con IL-2 o dopo ingaggio del TCR. Successivamente abbiamo valutato i cambiamenti nei principali fattori chiave della proliferazione, quali le cicline, nonché l’andamento di fattori trascrizionali come c-Fos e stat5, in seguito ad attivazione dei linfociti T. Tutti i pazienti osservati presentavano una evidente riduzione della proteina totale Crkl, cosi come una marcata riduzione della sua forma fosforilata. La fosforilazione di Crkl è indotta principalmente da IL-2 la quale è il principale fattore proliferativo dei linfociti T. IL-2 modula anche l’espressione di Crkl sia a livello di proteina che a livello di mRNA. In aggiunta, in questi soggetti, la proliferazione dei linfociti T dopo triggering del TCR appare anch’essa ridotta, se comparata a soggetti sani di controllo. Noi abbiamo anche osservato un decremento della fosforilazione di stat5 sempre a carico dei linfociti T dei pazienti, dopo stimolazione con IL-2. Stat5 è peraltro noto formare complessi trascrizionali con Crkl i quali complessi sono attivi in sede nucleare nella espressione di geni bersaglio. La successiva analisi dell’andamento dei fattori chiave che regolano il processo proliferativo ha rivelato un decremento nei livelli del fattore trascrizionale c-Fos, facente parte del complesso trascrizionale AP-1 e un calo, variabile nei livelli, della ciclina D3. Questi risultati si sono anche confermati su linee Jurkat dopo silenziamento specifico di Crkl. In conclusione la diminuita proliferazione, benchè solo parziale, osservata nei linfociti T dei pazienti si accompagna a decrementati livelli di Crkl, e fosfo-Crkl con conseguente riduzione anche del fattore trascrizionale c-Fos, e della ciclina D3. Nonché ad una ridotta fosforilazione di stat5, dopo stimolo con IL-2. Il nostro dato suggerisce un ruolo potenziale, ancorché non unico, di Crkl e della sua aploinsufficienza nelle alterazioni funzionali dei linfociti Te in particolare nel deficit proliferativo, in pazienti affetti da del22q11.2.XXVI Ciclo197

Supersymmetric gauge theories with decoupled operators and chiral ring stability

We propose a general way to complete supersymmetric theories with operators below the unitarity bound, adding gauge-singlet fields that enforce the decoupling of such operators. This makes it possible to perform all usual computations, and to compactify on a circle. We concentrate on a duality between an N=1 SU(2) gauge theory and the N=2 A_3 Argyres-Douglas theory, mapping the moduli space and chiral ring of the completed N=1 theory to those of the A_3 model. We reduce the completed gauge theory to 3D, finding a 3D duality with N=4 supersymmetric QED (SQED) with two flavors. The naive dimensional reduction is instead N=2 SQED. Crucial is a concept of chiral ring stability, which modifies the superpotential and allows for a 3D emergent global symmetry