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Résumé |
Abstract: In the planar limit of a large number of colors, N=4 Super-Yang-Mills theory becomes integrable and
certain scattering amplitudes and form factors can be computed to 8 loops. Due to known symmetries, the
first nontrivial amplitude in this theory is for six gluons. It can be bootstrapped to high loop order, using the
rigidity of the function space of multiple polylogarithms and information from integrability, namely the
pentagon OPE. A particular form factor, for the chiral stress-tensor operator to produce 3 gluons, can be
bootstrapped through 8 loops. This form factor is the N=4 analog of the LHC process, gluon gluon --> Higgs
+ gluon. Remarkably, the two quantities are related by a mysterious “antipodal” duality, which exchanges the
role of branch cuts and derivatives. Furthermore, this duality is “explained” by an antipodal self-duality of the
4-gluon form factor of the same operator. The self-duality has been verified through 3 loops.
Recently, antipodal self-duality has appeared in certain square fishnet integrals that govern 4-point
correlators in a strongly-deformed limit of planar N=4 SYM. However, we still don't know “who ordered”
antipodal (self-)duality, or what it really means. |
