[1][2] In 1984, Michael Green and John H. Schwarz realized that the anomaly in type I string theory with the gauge group SO(32) cancels because of an extra "classical" contribution from a 2-form field.
For the special choice of the gauge group SO(32) or E8 x E8, however, the anomaly factorizes and may be cancelled by a tree diagram.
The tree diagram describes the exchange of a virtual quantum of the B-field.
As recounted in The Elegant Universe's TV version, in the second episode, "The String's the Thing", section "Wrestling with String Theory", Green describes finding 496 on each side of the equals sign during a stormy night filled with lightning, and fondly recalls joking that "the gods are trying to prevent us from completing this calculation".
Anomalies in quantum theory arise from one-loop diagrams, with a chiral fermion in the loop and gauge fields, Ricci tensors, or global symmetry currents as the external legs.
These diagrams have the form of a triangle in 4 spacetime dimensions, which generalizes to a hexagon in D = 10, thus involving 6 external lines.
The interesting anomaly in SUSY D = 10 gauge theory is the hexagon which has a particular linear combination of the two-form gauge field strength and Ricci tensor,
Green and Schwarz realized that one can add a so-called Chern–Simons term to the classical action, having the form
(with space-time indices not contracted), which is precisely one of the factors appearing in the hexagon anomaly.
, when combined with a trilinear vertex through exchange of a gauge boson, has precisely the right variation to cancel the hexagon anomaly.