论文标题
在磁通量的多项式上，用于与等级5相关的梅尔文样解决方案
On fluxbrane polynomials for generalized Melvin-like solutions associated with rank 5 Lie algebras
论文作者
论文摘要
我们考虑了对应于等级的Lie代数$ 5 $（$ a_5 $，$ b_5 $，$ c_5 $，$ d_5 $）的普遍的类似梅尔文的解决方案。该解决方案在$ d $二维的重力模型中进行，具有五个Abelian 2形和五个标量场。它们由五个Moduli函数$ H_S（z）$（$ s = 1，...，5 $）的平方径向坐标$ z =ρ^2 $遵守五个差分主方程。模量功能是$（N_1，N_2，N_3，N_4，N_5）=（5,8,9,8,5），（10,18,24,28,15），（9,16,21,21,24,25），（8,14,14,18,18,10,10,10,10,10,10）$，$，A_55 $，A_55 $，A_55 $，A_5 $，A_5 $， $ C_5 $，$ D_5 $。多项式在大距离的渐近行为由一些整数价值$ 5 \ times 5 $ 5 $矩阵$ν$以某种方式与lie代数的cartan矩阵连接，并在$ a_5 $和$ d_5 $的情况下与$ \ semmrix的$ \ sry-matry of $ \ sry-ymry} commention-ymry} commention-ymry} Dynkin图。获得多项式的对称性和二元性身份，以及在较大距离的溶液中的渐近关系。
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.
