临界拓扑大质量引力中的可积族、Hurwitz数和分支点场
Integrable hierarchies, Hurwitz numbers and a branch point field in critical topologically massive gravity
摘要：
我们讨论了宇宙学临界拓扑质量引力的配分函数的对数贡献的可积方面。一方面，用描述集合划分统计的Bell多项式表示，对数域的配分函数是位势Burgers族的生成函数。另一方面，多项式变量是Kadomtsev-Petviashvili方程的解，并且配分函数是KP $τ$函数，使得被计数的对数场的孤子性质更精确。证明了配分函数是Hurwitz数的母函数，并导出了它的表达式。事实上，配分函数是分支覆盖的生成函数，使洞察orbifold目标空间。我们证明了对数域$ψ^{new}_{μν}$可以看作是与分支点$μl =1$相关联的分支点域。
英文摘要：
We discuss integrable aspects of the logarithmic contribution of the partition function of cosmological critical topologically massive gravity. On one hand, written in terms of Bell polynomials which describe the statistics of set partitions, the partition function of the logarithmic fields is a generating function of the potential Burgers hierarchy. On the other hand, the polynomial variables are solutions of the Kadomtsev-Petviashvili equation, and the partition function is a KP $τ$ function, making more precise the solitonic nature of the logarithmic fields being counted. We show that the partition function is a generating function of Hurwitz numbers, and derive its expression. The fact that the partition function is the generating function of branched coverings gives insight on the orbifold target space. We show that the logarithmic field $ψ^{new}_{μν}$ can be regarded as a branch point field associated to the branch point $μl =1$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
