Twoloop octagons, algebraic letters and Q ¯ equations
Abstract
We compute the symbol of the first twoloop amplitudes in planar N =4 SYM with algebraic letters, the eightpoint Next to Maximally Helicity Violating (NMHV) amplitude (or the dual octagon Wilson loops). We show how to apply Q ¯ equations of [S. CaronHuot and S. He, J. High Energy Phys. 07 (2012) 174, 10.1007/JHEP07(2012)174] for computing the differential of twoloop n point NMHV amplitudes and present the result for n =8 explicitly. The symbol alphabet for octagon consists of 180 independent rational letters and 18 algebraic ones involving Gramdeterminant square roots. We comment on allloop predictions for final entries and aspects of the result valid for all multiplicities.
 Publication:

Physical Review D
 Pub Date:
 March 2020
 DOI:
 10.1103/PhysRevD.101.061701
 Bibcode:
 2020PhRvD.101f1701H