Large-Scale Diffuse Intergalactic Magnetic Fields Constraints with the
  Cherenkov Telescope Array
  Magnetic fields of the order of $\mu$-Gauss are observationally detected in
galaxies and galaxy clusters, which can be (at least) in part originated by the
amplification of much weaker primordial seed fields. These fields should be
carried out by strong galactic outflows, magnetically enriching the
InterGalactic Medium (IGM). However direct observation of magnetic fields in
the IGM is scarce. This talk will give a review of how Intergalactic Magnetic
Field (IGMF) can be constrained using gamma-ray observations. High-energy TeV
photons emitted by distant blazars can interact with the cosmic extragalactic
optical/infrared/microwave background light, producing electron-positron pairs,
and initiating electromagnetic cascades in the IGM. The charged component of
these cascades is deflected by IGMFs, thereby reducing the observed point-like
TeV flux, and creating an extended image in the GeV energy range, which can
potentially be detected with $\gamma$-ray telescopes (Fermi-LAT, HESS, CTA).
Studies (e.g., Neronov & Vovk 2010, Dolag et al. 2011) have put lower limits on
the IGMF strength of the order of $10^{-16} - 10^{-15} G$, and filling factors
of $60\%$. This talk will describe the constraints which the Cherenkov
Telescope Array sensitivity is expected to give (CTA Consortium 2018).
