论文标题
$ \ MATHCAL {N} = 4 $ SYM，（SUPER） - POLYNOMIAL环和新兴的量子机械对称性
$\mathcal{N}=4$ SYM, (super)-polynomial rings and emergent quantum mechanical symmetries
论文作者
论文摘要
PSU $（2,2 | 4）$的半BP表示的结构导致了超级多项式环$ \ Mathcal {R}（8 | 8）$的定义，该$ \ Mathcal {R}（8 | 8）$，该$承认PSU $（2,2 | 4）$在超级环上的微分运算符中实现了。半bps基本字段表示的字符用$ \ Mathcal {r}（8 | 8）$的精确模块的精确序列编码表示表示的分辨率。半bps表示是通过通过二次理想来给超级环的标记来实现的，同样，将超级环的发电机中的某些二次多项式设置为零。对超级单位式戒指的PSU $（2,2 | 4）$的半BP基本场的不可约定表示的描述，是使用由标准升高运营商的通勤子空间生成的lie（Super-）代数（超级）代数的最低级别（超级）代数的示例。我们使用SU（3）和SU（4）表示的简单示例来说明构造。这些结果导致定义量子机械出现的概念，用于对称性的振荡器实现，该振荡器实现基于创建算子中多项式环中的理想。
The structure of half-BPS representations of psu$(2,2|4)$ leads to the definition of a super-polynomial ring $\mathcal{R}(8|8)$ which admits a realisation of psu$(2,2|4)$ in terms of differential operators on the super-ring. The character of the half-BPS fundamental field representation encodes the resolution of the representation in terms of an exact sequence of modules of $\mathcal{R}(8|8)$. The half-BPS representation is realized by quotienting the super-ring by a quadratic ideal, equivalently by setting to zero certain quadratic polynomials in the generators of the super-ring. This description of the half-BPS fundamental field irreducible representation of psu$(2,2|4)$ in terms of a super-polynomial ring is an example of a more general construction of lowest-weight representations of Lie (super-) algebras using polynomial rings generated by a commuting subspace of the standard raising operators, corresponding to positive roots of the Lie (super-) algebra. We illustrate the construction using simple examples of representations of su(3) and su(4). These results lead to the definition of a notion of quantum mechanical emergence for oscillator realisations of symmetries, which is based on ideals in the ring of polynomials in the creation operators.
