论文标题
单一矩阵模型的“ null-a”可缩短性
The "Null-A" superintegrability for monomial matrix models
论文作者
论文摘要
我们发现，在单个非高斯矩阵模型的异国情调扇区中，可固定性（角色扩展）属性持续存在，其潜在的$ \ tr x^r $，纯阶段，幼稚的分区函数$ \ langle 1 \ rangle $ nance vanish nishes。 （反常校正）分区功能的角色由$ \ left \langleχ_ρ\ right \ rangle $ - 适当选择的\ textit {squareit {square} partiton $ρ$的schur平均值;此类分区众所周知，对应于Virasoro代数的奇异向量。此外，非零是Schur平均值$ \ weft \ langle的χ_μ\ right \ rangle $，对于这种$ρ$的$ρ$作为其$ r $ core的$ρ$，并且更稳定性公式具有\ textit {skew} schur函数$χ_χ{μ/ρ} $的价值。到目前为止，相关的拓扑递归和Harer-Zagier公式的概括仍然晦涩。
We find that superintegrability (character expansion) property persists in the exotic sector of the monomial non-Gaussian matrix model, with potential $\Tr X^r$, in pure phase, where the naive partition function $\langle 1 \rangle$ vanishes. The role of the (anomaly-corrected) partition function is played by $\left\langleχ_ρ\right\rangle$ -- the Schur average of the suitably chosen \textit{square} partiton $ρ$; such partitions are well-known to correspond to singular vectors of the Virasoro algebra. Further, non-zero are only Schur averages $\left\langle χ_μ\right\rangle$ for such $μ$ that have $ρ$ as their $r$-core, and superintegrability formula features the value of the \textit{skew} Schur function $χ_{μ/ρ}$ at special point. The associated topological recursion and Harer-Zagier formula generalizations so far remain obscure.
