论文标题
Hilbert系列和$ O（n）$型号的高级拉格朗日
Hilbert series and higher-order Lagrangians for the $O(N)$ model
论文作者
论文摘要
我们将Hilbert系列方法与$ O（N）$非线性Sigma模型的高阶Lagrangians的明确结构进行了比较。我们使用Hilbert系列来查找质量尺寸16的操作员的数量和类型，对于时空尺寸$ D $，最高为12和$ n $，最高为12，并将操作员进一步将内部对称性组$ O（n）$的时空平等和奇偶校验分类。对于均等的平均值和其他三个案例的尺寸为10，操作员的明确构造均达到质量12。这两种方法的结果完全一致。这为希尔伯特系列的猜想提供了证据，涉及共同关闭但没有共同置换$ k $ - forms，这考虑了逐个方面的集成关系。
We compare the Hilbert series approach with explicit constructions of higher-order Lagrangians for the $O(N)$ nonlinear sigma model. We use the Hilbert series to find the number and type of operators up to mass dimension 16, for spacetime dimension $D$ up to 12 and $N$ up to 12, and further classify the operators into spacetime parity and parity of the internal symmetry group $O(N)$. The explicit construction of operators is done up to mass dimension 12 for both parities even and dimension 10 for the other three cases. The results of the two methods are in full agreement. This provides evidence for the Hilbert series conjecture regarding co-closed but not co-exact $k$-forms, which takes into account the integration-by-parts relations.
