(反)德西特空间中共形杨-米尔斯多重态的贝祖式退耦
Bezoutian Decoupling for Conformal Yang--Mills Multiplets in $(A)dS$
浏览论文内容
中文总结 AI 辅助
本文针对（反）德西特空间共形杨-米尔斯多重态，通过构造贝祖式延拓实现格拉姆形式对角化，推导了相关闭式公式，分析了N=4时的代数约束，拓展了共形杨-米尔斯理论的退耦形式。
中文摘要 AI 辅助
Metsaev 给出了六维、八维、十维（反）德西特空间中（A）dS共形杨-米尔斯理论的通用且退耦的形式，并猜想了更高偶数维下的对应关系。受附录C中低维矩阵的启发，我们识别并对角化了三种通用格拉姆形式的全N阶自然贝祖式延拓。首一汉克尔截断、附录C中的求值模式以及猜想的质量节点唯一确定了该延拓；其向量与根基格拉姆形式的对角化恒等式对所有D=d+1=2N+4（N≥1）成立。该延拓是z∏（i=1到N）(z-ρi(2N+1-i))与1的贝祖矩阵，在其单根处求值得到场重定义中出现的范德蒙德同余式；相同计算给出了逆矩阵、行列式和惯性矩的闭式公式，并将归一化权重与约翰逊图重数对应起来。通用形式中已指定的任意非线性系数代数都通过该基变换得到迁移，但该结果未在任意维度中构建此类代数。当N=4时，我们施加结合性、弗罗贝尼乌斯不变性及固定平直特化，这些代数约束仍在固定通用基中允许一个单参数族的两两不同乘积。
英文摘要
Metsaev exhibited generic and decoupled formulations of conformal Yang--Mills theory in $(A)dS_6$, $(A)dS_8$, and $(A)dS_{10}$, and conjectured the corresponding relations in higher even dimensions. Motivated by the low-dimensional matrices in Appendix C, we identify and diagonalize a natural all-$N$ Bezoutian continuation of the three generic Gram forms. The monic Hankel cutoff, the evaluation pattern in Appendix C, and the conjectured mass nodes determine this continuation uniquely. Its vector and radical Gram-form diagonalization identities hold for every $D=d+1=2N+4$, $N\geq1$. The continuation is the Bezout matrix of $z\prod_{i=1}^N(z-ρi(2N+1-i))$ and $1$; evaluation at its simple roots produces the Vandermonde congruence appearing in the field redefinition. The same calculation gives closed formulas for the inverse, determinant, and inertia, and identifies the normalization weights with Johnson-graph multiplicities. Any nonlinear coefficient algebra already specified in the generic formulation is transported by this change of basis. The result does not construct such an algebra in arbitrary dimension. At $N=4$, we impose associativity, Frobenius invariance, and a fixed flat specialization; these algebraic constraints still admit a one-parameter family of pairwise distinct products in a fixed generic basis.
