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Title:
The Quantum Inverse Scattering Method from 4d Chern-Simons Theory
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Abstract:
We elucidate the relationship between 2d integrable field theories and 2d integrable lattice models via the discretization of order surface operators to Wilson lines in 4d Chern-Simons theory. This provides a convenient framework to study the quantum integrability of a large class of classically integrable field theories in terms of integrable quantum spin chains, realizing and generalizing the quantum inverse scattering method of Faddeev and Reshetikhin. In particular, we show how lattice discretization can be realized, via perturbative 4d Chern-Simons theory, for the Faddeev-Reshetikhin model, the Zakharov-Mikhailov model, the massless Thirring model, sigma models on flag manifolds and odd-dimensional spheres, as well as the trigonometric and elliptic generalizations of these models. More generally, we describe how lattice discretization can be realized for a pair of affine vertex operator algebras. Anomalies that prevent the quantization of certain integrable field theories are interpreted as obstructions to converting a discretized surface operator into a collection of Wilson lines. Based on work with Junichi Sakamoto and Masahito Yamazaki.
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