Branes and Categorifying Integrable Lattice Models

DOI10.4310/ATMP.2020.V24.N1.A1zbMATH Open1518.81079arXiv1806.02821MaRDI QIDQ6302709

Meer Ashwinkumar, Meng-Chwan Tan, Qin Zhao

Publication date: 7 June 2018

Abstract: We elucidate how integrable lattice models described by Costello's 4d Chern-Simons theory can be realized via a stack of D4-branes ending on an NS5-brane in type IIA string theory, with D0-branes on the D4-brane worldvolume sourcing a meromorphic RR 1-form, and fundamental strings forming the lattice. This provides us with a nonperturbative integration cycle for the 4d Chern-Simons theory, and by applying T- and S-duality, we show how the R-matrix, the Yang-Baxter equation and the Yangian can be categorified, that is, obtained via the Hilbert space of a 6d gauge theory.

Mathematics Subject Classification ID

Quantum field theory on lattices (81T25) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Groups and algebras in quantum theory and relations with integrable systems (81R12) Lattice dynamics; integrable lattice equations (37K60) Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) (81T35)

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