This entry is about the article
on differential cohomology, higher gauge fields appearing in string theory and their quantum anomalies.
Motivated by attempting to fully formalize Green-Schwarz mechanism-type quantum anomaly problems previously studied by Edward Witten, this article introduced a systematic general definition for the refinement of any generalized (Eilenberg-Steenrod) cohomology theory to differential cohomology, the context for higher gauge fields in physics.
The connecton of this work to the physics of the electromagnetic field and of higher gauge fields in string theory was later developed further notably in
To this date generalized differential cohomology theories keep being studied mostly with motivation from string theory, but the work of Hopkins and Singer has put this subject on solid mathematical ground, and an independent mathematical field of differential cohomology is developing since then. See the list of references at differential cohomology.