Unitarization Technics in Hadron Physics with Historical Remarks

We review a series of unitarization techniques that have been used during the last decades, many of them in connection with the advent and development of current algebra and later of Chiral Perturbation Theory. Several methods are discussed like the generalized effective-range expansion, K-matrix approach, Inverse Amplitude Method, Pad\'e approximants and the N/D method. More details are given for the latter though. We also consider how to implement them in order to correct by final-state interactions. In connection with this some other methods are also introduced like the expansion of the inverse of the form factor, the Omn\'es solution, generalization to coupled channels and the Khuri-Treiman formalism, among others.Comment: 45 pages, 2 figures. Invited contribution to a special issue on "Effective Field Theories - Chiral Perturbation Theory and Non-relativistic QFT". Updated to match the published versio

S-duality resurgence in SL(2) Chern-Simons theory

We find that an S-duality in SL(2) Chern-Simons theory for hyperbolic 3-manifolds emerges by the Borel resummation of a semiclassical expansion around a particular flat connection associated to the hyperbolic structure. We demonstrate it numerically with two representative examples of hyperbolic 3-manifolds.Comment: 23 page

STiC -- A multi-atom non-LTE PRD inversion code for full-Stokes solar observations

The inference of the underlying state of the plasma in the solar chromosphere remains extremely challenging because of the nonlocal character of the observed radiation and plasma conditions in this layer. Inversion methods allow us to derive a model atmosphere that can reproduce the observed spectra by undertaking several physical assumptions. The most advanced approaches involve a depth-stratified model atmosphere described by temperature, line-of-sight velocity, turbulent velocity, the three components of the magnetic field vector, and gas and electron pressure. The parameters of the radiative transfer equation are computed from a solid ground of physical principles. To apply these techniques to spectral lines that sample the chromosphere, NLTE effects must be included in the calculations. We developed a new inversion code STiC to study spectral lines that sample the upper chromosphere. The code is based the RH synthetis code, which we modified to make the inversions faster and more stable. For the first time, STiC facilitates the processing of lines from multiple atoms in non-LTE, also including partial redistribution effects. Furthermore, we include a regularization strategy that allows for model atmospheres with a complex stratification, without introducing artifacts in the reconstructed physical parameters, which are usually manifested in the form of oscillatory behavior. This approach takes steps toward a node-less inversion, in which the value of the physical parameters at each grid point can be considered a free parameter. In this paper we discuss the implementation of the aforementioned techniques, the description of the model atmosphere, and the optimizations that we applied to the code. We carry out some numerical experiments to show the performance of the code and the regularization techniques that we implemented. We made STiC publicly available to the community.Comment: Accepted for publication in Astronomy & Astrophysic