论文标题
格拉斯曼尼亚人
The Grassmannian VOA
论文作者
论文摘要
我们研究了基于统一的Grassmannian Coset Cft $ \ Mathfrak {U} {U}（M+N）_K/（\ Mathfrak {U}（M）_K \ Times _K \ Times \ Times \ Mathfrak {u}（u}（u}（n）_k），我们研究了顶点操作员代数的3-参数家族。该VOA是一大批cosets的基本构建块，并概括了$ \ Mathcal {w} _ \ infty $代数。我们详细分析了表示形式及其角色，并在通用参数制度中找到了令人惊讶的简单字符公式，该公式允许使用优雅的组合配方。我们还讨论了代数的截断，并为完整的截断曲线提供了一个猜想的公式。我们开发了这些代数的粘合理论，以建立更复杂的固定和非coset代数。我们通过一些示例来证明这项技术的力量，并特别表明$ \ Mathcal {n} = 2 $ supersymmetric Grassmannian可以通过将三个波索尼克Grassmannian代数粘在循环中来获得。我们最终猜测，该代数是表现出柔性对称性的代数较大的代数家族的诱人可能性。这个猜想的家族的专业化应包括统一的格拉斯曼尼亚家庭以及拉格朗日格拉曼尼亚的VOA家族，该家族在单一和正骨上的coset中插值。
We study the 3-parametric family of vertex operator algebras based on the unitary Grassmannian coset CFT $\mathfrak{u}(M+N)_k/(\mathfrak{u}(M)_k \times \mathfrak{u}(N)_k)$. This VOA serves as a basic building block for a large class of cosets and generalizes the $\mathcal{W}_\infty$ algebra. We analyze representations and their characters in detail and find surprisingly simple character formulas for the representations in the generic parameter regime that admit an elegant combinatorial formulation. We also discuss truncations of the algebra and give a conjectural formula for the complete set of truncation curves. We develop a theory of gluing for these algebras in order to build more complicated coset and non-coset algebras. We demonstrate the power of this technology with some examples and show in particular that the $\mathcal{N}=2$ supersymmetric Grassmannian can be obtained by gluing three bosonic Grassmannian algebras in a loop. We finally speculate about the tantalizing possibility that this algebra is a specialization of an even larger 4-parametric family of algebras exhibiting pentality symmetry. Specialization of this conjectural family should include both the unitary Grassmannian family as well as the Lagrangian Grassmannian family of VOAs which interpolates between the unitary and the orthosymplectic cosets.
