Fundamental High Energy Physics has been mainly driven by the high energy fermionic colliding beam paradigm. Today the possibility to amplify laser to extreme energy and peak power offers, in addition to possibly more compact and cheaper ways to help HEP, a suit of complementary new alternatives underpinned by single shot, large field laser pulse, that together we could call Laser-based High Field Fundamental Physics. The main mission of the International center on Zetta-Exawatt Science and Technology (IZEST) is to muster the scientific community behind this new concept. As an example, we project to use the laser field to probe the nonlinearity of vacuum due to nonlineairities and light-mass weak coupling fields such as Heisenberg-Euler QED, dark matter and dark energy.
