Advances in Theoretical and Mathematical Physics

Volume 24 (2020)

Number 8

The second of two special issues in honor of Cumrun Vafa’s 60th birthday

Unification of integrability in supersymmetric gauge theories

Pages: 1931 – 2041



Kevin Costello (Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada)

Junya Yagi (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)


A four-dimensional analog of Chern–Simons theory produces integrable lattice models from Wilson lines and surface operators. We show that this theory describes a quasi-topological sector of maximally supersymmetric Yang–Mills theory in six dimensions, topologically twisted and subjected to an $\Omega$-deformation. By realizing the six-dimensional theory in string theory and applying dualities, we unify various phenomena in which the eight-vertex model and the XYZ spin chain, as well as variants thereof, emerge from supersymmetric gauge theories.

This work is supported by the NSERC Discovery Grant program and by the Perimeter Institute for Theoretical Physics. Part of the research was conducted while JY was supported by the ERC Starting Grant No. 335739 “Quantum fields and knot homologies” funded by the European Research Council under the European Union’s Seventh Framework Programme and by the National Key Research and Development Program of China (No. 2020YFA0713000). Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.

Published 28 September 2021