Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 7

Special Issue: Proceedings of the Strings 2016 Conference in Beijing

Guest Editors: J. Maldacena (Institute for Advanced Study), H. Ooguri (California Institute of Technology), H. Babak (Harvard University), S. Li (Tsinghua University), W. Song (Tsinghua University), and H. Lin (Tsinghua University)

Integrable lattice models from gauge theory

Pages: 1819 – 1843

DOI: https://dx.doi.org/10.4310/ATMP.2017.v21.n7.a10

Author

Edward Witten (School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey, U.S.A.)

Abstract

These notes provide an introduction to recent work by Kevin Costello in which integrable lattice models of classical statistical mechanics in two dimensions are understood in terms of quantum gauge theory in four dimensions. This construction will be compared to the more familiar relationship between quantum knot invariants in three dimensions and Chern–Simons gauge theory. (Based on a Whittaker Colloquium at the University of Edinburgh and a lecture at Strings 2016 in Beijing.)

Full Text (PDF format)

Research supported in part by NSF Grant PHY-1606531. I thank K. Costello, J. Perk, and M. Yamazaki for useful comments.

Published 19 March 2018