Quantum Spectral Curve of N=4 SYM and Conformal Fishnet Theory

I will give an overview of exact solution for the spectrum of anomalous dimensions of planar N=4 SYM theory known as Quantum Spectral Curve (QSC). I will apply it to a special, chiral limit of N=4 SYM combining week coupling and strong gamma-deformation (with imaginary parameters), recently proposed by Gurdogan and myself.  The limit gives rise to a new class of non-unitary integrable CFTs of logarithmic type in 4 dimensions, the simplest of them being the so called bi-scalar theory. It is dominated by a very limited set of integrable "fishnet" Feynman graphs at any loop order. The explicit underlying structure of this integrability is related to the quantum conformal SU(2,2) Heisenberg spin chain.  I will present   the analytic and numerical results for anomalous dimensions of BMN-type operators dominated by calculable "wheel" graphs. I will also mention the precise Yangian symmetry of planar bi-scalar amplitudes.