In the 1980s, Álvarez-Gaumé had various important contributions to the field of string theory and its mathematical framework. Together with Edward Witten he showed in 1983 that quantum field theories generally have gravitational anomalies.[1] Shortly after this, Michael Green and John Schwarz showed that such anomalies are avoided in various realizations of superstring theory. Álvarez-Gaumé is also known for a physical proof of the Atiyah–Singer theorem using supersymmetry.
His work spans a range of different subjects, including string perturbation theory at higher orders, quantum field theories on Riemann surfaces,[2]
quantum groups, as well as dualities in string theory and black holes in string theory.[3][4]
In the 1990s, Álvarez-Gaumé studied supersymmetry breaking at low energies (in N = 2 SUSY gauge theories).[5][6] He has also co-authored a textbook on quantum field theory.[7]