FTheory: High-Loop Perturbative QFT from Integrability
The planar N=4 SYM is believed to be integrable. Following this thoroughly justified belief, its exact spectrum at finite coupling had been encoded recently into a quantum spectral curve -- a concise set of Riemann-Hilbert equations. We can explicitly solve the quantum spectral curve in various regimes. In particular, it is possible to perform a highly-efficient weak coupling expansion producing anomalous dimensions at 6,7,8,9 loops and beyond, as well as proving several results about the structure of the answer at any loop order.