论文标题
来自非交通性几何形状的可集成模型，应用到3D双重性
Integrable Models From Non-Commutative Geometry With Applications to 3D Dualities
论文作者
论文摘要
我们讨论了通过内部变形构建的新的强质同苯二代数。这种变形具有许多显着的特性。在最简单的情况下，每一个共同代数的单参数家族都会导致$ l_ \ infty $ -Algebra，可用于构建经典的集成模型。此类$ l_ \ infty $ - 代数的另一个应用与Chern-simons矢量模型中的三维隆体化二元性有关，在该模型中，它实现了稍微破裂的更高自旋对称性的想法。一大类的关联代数源自泊松歧管的变形量化。但是，$ 3D $ - 实用二元性的应用需要扩展到泊松孔的变形量化的扩展，这是一个空旷的问题。 $ 3D $ - 实用双重性可以通过证明$ l_ \ infty $ -Algebra的独特类别可以用作相关功能来证明。
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 $L_\infty$-algebra that can be used to construct a classical integrable model. Another application of this class of $L_\infty$-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 $L_\infty$-algebra that can serve as correlation functions.
