论文标题
Ising模型的单数支持
The singular support of the Ising model
论文作者
论文摘要
我们证明了Ising模型顶点代数的特征的新的费米金准粒子总和表达式，与Rogers-ramanujan类型的Jackson-Slater $ Q $ Q $ series的身份以及与Matrix $ \ left的NAHM和NAHM总和有关（\ smallmatrix} 8＆3＆3;作为后果，我们发现了Ising模型的明确基础，以及对其单一支持的描述。我们发现，后者的理想捆扎将其定义为其相关方案的弧形空间的子处理，是有限地生成的，它是一种差异理想。我们证明了与中央电费的Virasoro Lie lie代数相关的Rogers-Ramanujan-Slater类型的三个新的$ Q $ Series标识。我们对与真空模块相关的身份进行组合解释。
We prove a new Fermionic quasiparticle sum expression for the character of the Ising model vertex algebra, related to the Jackson-Slater $q$-series identity of Rogers-Ramanujan type and to Nahm sums for the matrix $\left( \begin{smallmatrix} 8 & 3 \\ 3 & 2 \end{smallmatrix} \right)$. We find, as consequences, an explicit monomial basis for the Ising model, and a description of its singular support. We find that the ideal sheaf of the latter, defining it as a subscheme of the arc space of its associated scheme, is finitely generated as a differential ideal. We prove three new $q$-series identities of the Rogers-Ramanujan-Slater type associated with the three irreducible modules of the Virasoro Lie algebra of central charge $1/2$. We give a combinatorial interpretation to the identity associated with the vacuum module.
