Wilson Loops and Chiral Correlators on Squashed Sphere

We study chiral deformations of ${\cal N}=2$ and ${\cal N}=4$ supersymmetric gauge theories obtained by turning on $\tau_J \,{\rm tr} \, \Phi^J$ interactions with $\Phi$ the ${\cal N}=2$ superfield. Using localization, we compute the deformed gauge theory partition function $Z(\vec\tau|q)$ and the expectation value of circular Wilson loops $W$ on a squashed four-sphere. In the case of the deformed ${\cal N}=4$ theory, exact formulas for $Z$ and $W$ are derived in terms of an underlying $U(N)$ interacting matrix model replacing the free Gaussian model describing the ${\cal N}=4$ theory. Using the AGT correspondence, the $\tau_J$-deformations are related to the insertions of commuting integrals of motion in the four-point CFT correlator and chiral correlators are expressed as $\tau$-derivatives of the gauge theory partition function on a finite $\Omega$-background. In the so called Nekrasov-Shatashvili limit, the entire ring of chiral relations is extracted from the $\epsilon$-deformed Seiberg-Witten curve. As a byproduct of our analysis we show that $SU(2)$ gauge theories on rational $\Omega$-backgrounds are dual to CFT minimal models.Comment: 33 pages, 2 figure, in this version we have added two new references and a detailed comparison with the results obtained in one of these tw

Efficiency of Human Activity on Information Spreading on Twitter

Understanding the collective reaction to individual actions is key to effectively spread information in social media. In this work we define efficiency on Twitter, as the ratio between the emergent spreading process and the activity employed by the user. We characterize this property by means of a quantitative analysis of the structural and dynamical patterns emergent from human interactions, and show it to be universal across several Twitter conversations. We found that some influential users efficiently cause remarkable collective reactions by each message sent, while the majority of users must employ extremely larger efforts to reach similar effects. Next we propose a model that reproduces the retweet cascades occurring on Twitter to explain the emergent distribution of the user efficiency. The model shows that the dynamical patterns of the conversations are strongly conditioned by the topology of the underlying network. We conclude that the appearance of a small fraction of extremely efficient users results from the heterogeneity of the followers network and independently of the individual user behavior.Comment: 29 pages, 10 figure

Analysis of the h,H,A→τμh, H, A \to \tau \mu decays induced from SUSY loops within the Mass Insertion Approximation

In this paper we study the lepton favor violating decay channels of the neutral Higgs bosons of the Minimal Supersymmetric Standard Model into a lepton and an anti-lepton of different flavor. We work in the context of the most general flavor mixing scenario in the slepton sector, in contrast to the minimal flavor violation assumption more frequently used. Our analytic computation is a one-loop diagrammatic one, but in contrast to the full one-loop computation which is usually referred to the physical slepton mass basis, we use here instead the Mass Insertion Approximation (MIA) which uses the electroweak interaction slepton basis and treats perturbatively the mass insertions changing slepton flavor. By performing an expansion in powers of the external momenta in the relevant form factors, we will be able to separate explicitly in the analytic results the leading non-decoupling (constant at asymptotically large sparticle masses) and the next to leading decoupling contributions (decreasing with the sparticle masses). Our final aim is to provide a set of simple analytic formulas for the form factors and the associated effective vertices, that we think may be very useful for future phenomenological studies of the lepton flavor violating Higgs boson decays, and for their comparison with data. The accuracy of the numerical results obtained with the MIA are also analyzed and discussed here in comparison with the full one-loop results. Our most optimistic numerical estimates for the three neutral Higgs boson decays channels into $\tau$ and $\mu$ leptons, searching for their maximum rates that are allowed by present constraints from $\tau \to \mu \gamma$ data and beyond Standard Model Higgs boson searches at the LHC, are also included.Comment: 37 pages, 16 figures, 3 appendices. This version v3 matches the manuscript published in JHE

Dynamical Supersymmetry Breaking in Intersecting Brane Models

In this paper we study dynamical supersymmetry breaking in absence of gravity with the matter content of the minimal supersymmetric standard model. The hidden sector of the theory is a strongly coupled gauge theory, realized in terms of microscopic variables which condensate to form mesons. The supersymmetry breaking scalar potential combines F, D terms with instanton generated interactions in the Higgs-mesons sector. We show that for a large region in parameter space the vacuum breaks in addition to supersymmetry also electroweak gauge symmetry. We furthermore present local D-brane configurations that realize these supersymmetry breaking patterns.Comment: 30 pages, 4 figures, pdflate