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A bstract We consider the N = 2 SYM theory with gauge group SU( N ) and a matter content consisting of one multiplet in the symmetric and one in the anti-symmetric representation. This conformal theory admits a large- N ’t Hooft expansion and is dual to a particular orientifold of AdS 5 × S 5 . We analyze this gauge theory relying on the matrix model provided by localization à la Pestun. Even though this matrix model has very non-trivial interactions, by exploiting the full Lie algebra approach to the matrix integration, we show that a large class of observables can be expressed in a closed form in terms of an infinite matrix depending on the ’t Hooft coupling λ . These exact expressions can be used to generate the perturbative expansions at high orders in a very efficient way, and also to study analytically the leading behavior at strong coupling. We successfully compare these predictions to a direct Monte Carlo numerical evaluation of the matrix integral and to the Padé resummations derived from very long perturbative series, that turn out to be extremely stable beyond the convergence disk | λ | < π 2 of the latter.

A bstract In a N = 2 superconformal gauge theory with matter hypermultiplets transforming in the symmetric and anti-symmetric representations of SU( N ), we study the integrated correlators of two Coulomb-branch operators and two moment-map operators using localization. In the corresponding matrix model we identify the operator associated with the integrated insertions of moment-map operators and provide for it an exact expression valid for all values of the coupling constant in the planar limit. This allows us to study the integrated correlators at strong-coupling where we show that they behave as the 2-point functions of the Coulomb-branch operators, up to an overall constant dependent only on the conformal dimensions of the latter. The strong-coupling relation between integrated correlators and 2-point functions turns out to be the same as in N = 4 SYM at large N , despite the reduced amount of supersymmetry in our theory.

A bstract We consider N = 2 superconformal quiver gauge theories in four dimensions and evaluate the chiral/anti-chiral correlators of single-trace operators. We show that it is convenient to form particular twisted and untwisted combinations of these operators suggested by the dual holographic description of the theory. The various twisted sectors are orthogonal and the correlators in each sector have always the same structure, as we show at the lowest orders in perturbation theory with Feynman diagrams. Using localization we then map the computation to a matrix model. In this way we are able to obtain formal expressions for the twisted correlators in the planar limit that are valid for all values of the ‘t Hooft coupling λ , and find that they are proportional to 1 /λ at strong coupling. We successfully test the correctness of our extrapolation against a direct numerical evaluation of the matrix model and argue that the 1 /λ behavior qualitatively agrees with the holographic description.

A bstract We consider two four-dimensional SCFTs with gauge group Sp( N ): the N = 4 SYM theory and the N = 2 theory with four hypermultiplets in the fundamental representation and one hypermultiplet in the rank-2 antisymmetric representation of the gauge group. Using supersymmetric localization and by exploiting a Toda equation, we compute the integrated correlator between a half-BPS Wilson line and two moment map operators of conformal dimension 2. We obtain exact expressions for this observable, valid for any value of the ’t Hooft coupling in the large N -limit of the theory and we derive the corresponding strong coupling expansions.

A bstract We study the 3-point functions of gauge-invariant scalar operators in four dimensional N = 2 superconformal quiver theories using supersymmetric localization in the planar limit of a large number of colors. By exploiting a web of nontrivial relations, we show that the 3-point functions can be expressed in terms of the 2-point functions through exact Ward-like identities that are valid for all values of the coupling constant. In this way, using recent results about the 2-point functions, we are able to obtain the asymptotic strong-coupling expansion of the 3-point functions and of the corresponding structure constants in the planar limit. Our results extend to sub-leading orders what has been recently found at leading order, where a precise match with calculations within the AdS/CFT correspondence at the supergravity level is possible. Therefore, our findings can be interpreted also as a prediction for the sub-leading string corrections to these holographic calculations.

A bstract The D theory is a N = 2 conformal SYM theory in four dimensions with gauge group SU( N ), four matter hypermultiplets in the fundamental and two in the anti-symmetric representation, and a flavor symmetry that contains a U(4) factor. Its holographic dual is obtained via a combination of orbifold and orientifold projections from Type II B string theory on AdS 5 × S 5 and possesses a sector of open strings attached to D7 branes with U(4) Chan-Paton factors. The AdS Veneziano amplitude of the U(4) gluons is dual to four-point correlators of moment-map operators of the U(4) flavor symmetry in the D theory. An integrated version of these correlators is captured by a deformation of the D theory in which the fundamental hypermultiplets acquire a mass. The partition function of this massive theory can be evaluated with matrix-model techniques using localization. In this paper we analyze the matrix model of the mass-deformed D theory arising from localization using the so-called “full Lie algebra” approach in a 1/ N expansion. In particular, we study the partition function and its mass derivatives up to O (1/ N 2 ) corrections obtaining exact expressions that are valid for all values of the ’t Hooft coupling. We also analyze their behavior at strong coupling where our results produce useful constraints on the dual open string scattering amplitudes in AdS.

A bstract We study the 3-point functions of single-trace scalar operators in a four-dimensional N = 2 SYM theory with gauge group SU( N ) and matter in the symmetric plus anti-symmetric representation, which has a vanishing β -function. By mapping this computation to the matrix model arising from localization on a 4-sphere we are able to resum the perturbative expansion in the large- N ’t Hooft limit and derive the behavior of the correlators at strong coupling. Finally, by combining our results on the 3-point functions with those on the 2-point functions that have been recently found, we obtain the normalized 3-point coefficients of this conformal field theory at strong coupling and find that they depend in a simple way on the conformal dimensions of the single-trace operators.

A bstract Building on [ 1 ], we uncover new properties of type-B conformal anomalies for Coulomb-branch operators in continuous families of 4D N = 2 SCFTs. We study a large class of such anomalies on the Higgs branch, where conformal symmetry is spontaneously broken, and compare them with their counterpart in the CFT phase. In Lagrangian the- ories, the non-perturbative matching of the anomalies can be determined with a weak coupling Feynman diagram computation involving massive multi-loop banana integrals. We extract the part corresponding to the anomalies of interest. Our calculations support the general conjecture that the Coulomb-branch type-B conformal anomalies always match on the Higgs branch when the IR Coulomb-branch chiral ring is empty. In the opposite case, there are anomalies that do not match. An intriguing implication of the mismatch is the existence of a second covariantly constant metric on the conformal manifold (other than the Zamolodchikov metric), which imposes previously unknown restrictions on its holonomy group.

Abstract We study 4-dimensional N 𝓝 = 2 superconformal quiver gauge theories obtained with an orbifold projection from N 𝓝 = 4 SYM, and compute the 2- and 3-point correlation functions among chiral/anti-chiral single-trace scalar operators and the corresponding structure constants. Exploiting localization, we map the computation to an interacting matrix model and obtain expressions for the correlators and the structure constants that are valid for any value of the ’t Hooft coupling in the planar limit of the theory. At strong coupling, these expressions simplify and allow us to extract the leading behavior in an analytic way. Finally, using the AdS/CFT correspondence, we compute the structure constants from the dual supergravity theory and obtain results that perfectly match the strong-coupling predictions from localization.

Background Inflammatory Bowel Diseases (IBD) are known to occur in association with Hirschsprung disease (HSCR). Most of cases are represented by Crohn Disease (CD) occurring in patients with Total Colonic Aganglionosis (TCSA) with an estimated prevalence of around 2%. Based on these considerations and on a number of provisional data belonging to our Center for Digestive Diseases, we developed a unicentric cross-sectional observational study aimed at describing phenotype, genotype, pathology and metagenomics of all patients with TCSA and Crohn-like lesions. Results Out of a series of 62 eligible TCSA patients, 48 fulfilled inclusion criteria and were enrolled in the study. Ten patients did not complete the study due to non-compliance or withdrawal of consent and were subsequently dropped out. A total of 38 patients completed the study. All patients were tested for chronic intestinal inflammation by a combination of fecal calprotectine (FC) or occult fecal blood (OFB) and underwent fecal metagenomics. Nineteen (50%) tested positive for FC, OFB, or both and subsequently underwent retrograde ileoscopy. Fourteen patients (36.8%) presented Crohn-like lesions, occurring after a median of 11.5 years after surgery (range 8 months − 21.5 years). No statistically significant differences regarding demographic, phenotype and genotype were observed comparing patients with and without lesions, except for need for blood transfusion that was more frequent in those with lesions. Faecal microbiome of patients with lesions (not that of caregivers) was less biodiverse and characterized by a reduction of Bacteroidetes , and an overabundance of Proteobacteria . FC tested negative in 3/14 patients with lesions (21%). Conclusions Our study demonstrated an impressive 10-folds higher incidence of chronic inflammation in TCSA. Up to 50% of patients may develop IBD-like lesions postoperatively. Nonetheless, we failed in identifying specific risk factors to be used to implement prevention strategies. Based on the results of our study, we suggest screening all TCSA patients with retrograde ileoscopy regardless of FC/OFB values. The frequency of endoscopic assessments and the role of FC/OFB screening in prompting endoscopy is yet to be determined.