秩5李代数广义Melvin型解的流膜多项式
On fluxbrane polynomials for generalized Melvin-like solutions associated with rank 5 Lie algebras
摘要：
考虑秩为$5$（$A_5$，$B_5$，$C_5$，$D_5$）的李代数的广义Melvin-like解.在$D$维引力模型中，我们得到了五个阿贝尔2-形式和五个标量场的解.它们由五个模函数$H_s(z)$（$s = 1,...,5$）的平方径向坐标$z=ρ^2$服从五个微分主方程。模函数分别是李代数$A_5$、$B_5$、$C_5$、$D_5$的幂多项式$(n_1, n_2, n_3, n_4, n_5) = (5,8,9,8,5), (10,18,24,28,15), (9,16,21,24,25), (8,14,18,10,10)$。在大距离的多项式的渐近行为是由一些整数值$5 \times 5$矩阵$ν$以某种方式连接的逆Cartan矩阵的李代数和（在$A_5$和$D_5$的情况下）与矩阵代表的发电机的$\mathbb{Z}_2$ -群对称的Dynkin图。得到了多项式的对称性和对偶性恒等式，以及解在大距离处的渐近关系。
英文摘要：
We consider generalized Melvin-like solutions corresponding to Lie algebras of rank $5$ ($A_5$, $B_5$, $C_5$, $D_5$). The solutions take place in $D$-dimensional gravitational model with five Abelian 2-forms and five scalar fields. They are governed by five moduli functions $H_s(z)$ ($s = 1,...,5$) of squared radial coordinate $z=ρ^2$ which obey five differential master equations. The moduli functions are polynomials of powers $(n_1, n_2, n_3, n_4, n_5) = (5,8,9,8,5), (10,18,24,28,15), (9,16,21,24,25), (8,14,18,10,10)$ for Lie algebras $A_5$, $B_5$, $C_5$, $D_5$ respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued $5 \times 5$ matrix $ν$ connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in $A_5$ and $D_5$ cases) with the matrix representing a generator of the $\mathbb{Z}_2$-group of symmetry of the Dynkin diagram. The symmetry and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances.
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