2022/04/19 by Alexey Sharapov, Sharapov, Alexey, Evgeny Skvortsov +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.2204.08903
20 pages; Corfu Summer Institute 2021 proceedings; few refs added
arxiv created 2022/05/02 · arxiv updated 2022/05/03
We discuss a new class of strong homotopy algebras constructed via inner deformations. Such deformations have a number of remarkable properties. In the simplest case, every one-parameter family of associative algebras leads to an L_∞-algebra that can be used to construct a classical integrable model. Another application of this class of L_∞-algebras is related with the three-dimensional bosonization duality in Chern--Simons vector models, where it implements the idea of the slightly-broken higher spin symmetry. One large class of associative algebras originates from Deformation Quantization of Poisson Manifolds. Applications to the 3d-bosonization duality require, however, an extension to deformation quantization of Poisson Orbifolds, which is an open problem. The 3d-bosonization duality can be proven by showing that there is a unique class of invariants of the L_∞-algebra that can serve as correlation functions.