S-duality and the prepotential in N=2* theories (I): the ADE algebras

The prepotential of N=2* supersymmetric theories with unitary gauge groups in an Omega-background satisfies a modular anomaly equation that can be recursively solved order by order in an expansion for small mass. By requiring that S-duality acts on the prepotential as a Fourier transform we generalise this result to N=2* theories with gauge algebras of the D and E type and show that their prepotentials can be written in terms of quasi-modular forms of SL(2,Z). The results are checked against microscopic multi-instanton calculus based on localization for the A and D series and reproduce the known 1-instanton prepotential of the pure N=2 theories for any gauge group of ADE type. Our results can also be used to obtain the multi-instanton terms in the exceptional theories for which the microscopic instanton calculus and the ADHM construction are not available.Comment: 33 pages, LaTeX2e, added references, version to be published in JHE

BPS wilson loops in generic conformal N = 2 SU(N) SYM theories

We consider the 1/2 BPS circular Wilson loop in a generic N = 2 SU(N) SYM theory with conformal matter content. We study its vacuum expectation value, both at finite N and in the large-N limit, using the interacting matrix model provided by localization results. We single out some families of theories for which the Wilson loop vacuum expectation values approaches the N = 4 result in the large-N limit, in agreement with the fact that they possess a simple holographic dual. At finite N and in the generic case, we explicitly compare the matrix model result with the field-theory perturbative expansion up to order g^8 for the terms proportional to the Riemann value zeta(5), finding perfect agreement. Organizing the Feynman diagrams as suggested by the structure of the matrix model turns out to be very convenient for this computation

Integrated correlators with a Wilson line in N= 4 SYM

In the context of integrated correlators in N= 4 SYM, we study the 2-point functions of local operators with a superconformal line defect. Starting from the mass-deformed N= 2* theory in presence of a 1/2-BPS Wilson line, we exploit the residual superconformal symmetry after the defect insertion, and show that the massive deformation corresponds to integrated insertions of the superconformal primaries belonging to the stress tensor multiplet with a specific integration measure which is explicitly derived after enforcing the superconformal Ward identities. Finally, we show how the Wilson line integrated correlator can be computed by the N= 2* Wilson loop vacuum expectation value on a 4-sphere in terms of a matrix model using supersymmetric localization. In particular, we reformulate previous matrix model computations by making use of recursion relations and Bessel kernels, providing a direct link with more general localization computations in N= 2 theories

Emitted radiation and geometry

In conformal N = 2 Super Yang-Mills theory, the energy emitted by an accelerated heavy particle is computed by the one-point function of the stress tensor operator in the presence of a Wilson line. In this paper, we consider the theory on the ellipsoid and we prove a conjectured relation between the stress tensor one-point function and the firrst order expansion of the Wilson loop expectation value in the squashing parameter. To do this, we analyze the behavior of the Wilson loop for a small deformation of the background geometry and, at firrst order in the deformation, we fix the kinematics using defect CFT constraints. In the final part of the paper, we analyze the consequences of our results for the weak coupling perturbative expansion. In particular, comparing the weakly coupled matrix model with the ordinary Feynman diagram expansion, we find a natural transcendentality driven organization for the latter

Integrated correlators with a Wilson line in N=4\mathcal{N}=4 SYM

In the context of integrated correlators in $\mathcal{N}=4$ SYM, we study the 2-point functions of local operators with a superconformal line defect. Starting from the mass-deformed $\mathcal{N}=2^*$ theory in presence of a $\frac{1}{2}$-BPS Wilson line, we exploit the residual superconformal symmetry after the defect insertion, and show that the massive deformation corresponds to integrated insertions of the superconformal primaries belonging to the stress tensor multiplet with a specific integration measure which is explicitly derived after enforcing the superconformal Ward identities. Finally, we show how the Wilson line integrated correlator can be computed by the $\mathcal{N}=2^*$ Wilson loop vacuum expectation value on a 4-sphere in terms of a matrix model using supersymmetric localization. In particular, we reformulate previous matrix model computations by making use of recursion relations and Bessel kernels, providing a direct link with more general localization computations in $\mathcal{N}=2$ theories.Comment: 34 pages, 1 figur

Trace checking of Metric Temporal Logic with Aggregating Modalities using MapReduce

Modern complex software systems produce a large amount of execution data, often stored in logs. These logs can be analyzed using trace checking techniques to check whether the system complies with its requirements specifications. Often these specifications express quantitative properties of the system, which include timing constraints as well as higher-level constraints on the occurrences of significant events, expressed using aggregate operators. In this paper we present an algorithm that exploits the MapReduce programming model to check specifications expressed in a metric temporal logic with aggregating modalities, over large execution traces. The algorithm exploits the structure of the formula to parallelize the evaluation, with a significant gain in time. We report on the assessment of the implementation - based on the Hadoop framework - of the proposed algorithm and comment on its scalability.Comment: 16 pages, 6 figures, Extended version of the SEFM 2014 pape

Correlators between Wilson loop and chiral operators in N=2 conformal gauge theories

We consider conformal N=2 super Yang-Mills theories with gauge group SU(N) and Nf=2N fundamental hypermultiplets in presence of a circular 1/2-BPS Wilson loop. It is natural to conjecture that the matrix model which describes the expectation value of this system also encodes the one-point functions of chiral scalar operators in presence of the Wilson loop. We obtain evidence of this conjecture by successfully comparing, at finite N and at the two-loop order, the one-point functions computed in field theory with the vacuum expectation values of the corresponding normal-ordered operators in the matrix model. For the part of these expressions with transcendentality zeta(3), we also obtain results in the large-N limit that are exact in the 't Hooft coupling lambda.Comment: 37 pages, 10 figures. v2: typo corrected, 3 references added. Version to appear on JHE