论文标题
$ \ Mathcal {n} = 4 $ super-yang-mills的近bps角相互作用的对称结构
Symmetry structure of the interactions in near-BPS corners of $ \mathcal{N} = 4$ super-Yang-Mills
论文作者
论文摘要
我们考虑$ \ Mathcal {n} = 4 $ super-yang-mills（sym）理论的限制，该理论接近bps界限。这些限制导致非依赖性的近BP理论描述了BPS边界附近的有效动力学和量化时称为自旋基质理论。可以通过在三个球员上减少$ \ Mathcal {n} = 4 $ SYM并整合在限制中变得非动态的字段来获得近BPS理论。我们使用$ \ mathrm {su}（1,2 | 2）$对称性执行近BPS限制的球体减少，与先前考虑的$ \ MATHRM {SURM {SU}（1,1）$对称性相比，它具有多个新功能，包括动态规格字段。我们在交互项的经典限制中发现了一个新结构。我们表明，交互项是由某些块构建的，该块包含$ \ mathrm {su}（1,2 | 2）$ algebra的不可约表示。此外，整个互动项可以解释为该表示的线性空间中的规范，并解释其功能，包括积极的确定性。这意味着人们可以将交互项视为与饱和BPS结合的距离。 $ \ mathrm {su}（1,1 | 1）$近-BPS理论及其子案例可以继承这些功能。这些观察结果指出了解决这些近BP理论的强耦合动力学的一种方法。
We consider limits of $\mathcal{N} = 4$ super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic near-BPS theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix theories. The near-BPS theories can be obtained by reducing $\mathcal{N}=4$ SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. We perform the sphere reduction for the near-BPS limit with $\mathrm{SU}(1,2|2)$ symmetry, which has several new features compared to the previously considered cases with $\mathrm{SU}(1,1)$ symmetry, including a dynamical gauge field. We discover a new structure in the classical limit of the interaction term. We show that the interaction term is built from certain blocks that comprise an irreducible representation of the $\mathrm{SU}(1,2|2)$ algebra. Moreover, the full interaction term can be interpreted as a norm in the linear space of this representation, explaining its features including the positive definiteness. This means one can think of the interaction term as a distance squared from saturating the BPS bound. The $\mathrm{SU}(1,1|1)$ near-BPS theory, and its subcases, is seen to inherit these features. These observations point to a way to solve the strong coupling dynamics of these near-BPS theories.
