论文标题
来自投影空间的束束的六维超级人
Six-dimensional supermultiplets from bundles on projective spaces
论文作者
论文摘要
六维最小超对称代数中的零零元素的投影变化是同构与$ \ mathbb {p}^1 \ times \ times \ mathbb {p}^3 $。我们将这个事实与纯旋转超级场形式主义一起研究六个维度的超级人，从投影空间上的向量束开始。我们对超级译本代数的不变式衍生成的所有多重组进行了分类。人们可以想到多重运动是那些在时空上的圆锥形曲折表现上排名第一的人。此外，我们明确地构建了与天然高级近似矢量束相关的多重组，包括切线和正常束及其双重束。在构建的多重组中，矢量多重和超级人数是$ \ Mathcal {o}（n）$ - 多重组的家族，以及超级重力和Gravitino多重组。一路上，我们解决了纯旋转超级场外形式主义中的各种理论问题。特别是，我们就投影性的尼尔肽品种与多重组的关系进行了一些一般性讨论，并在纯旋转超级赛义形式主义的背景下，在短束束带和二元性上证明了一般结果。
The projective variety of square-zero elements in the six-dimensional minimal supersymmetry algebra is isomorphic to $\mathbb{P}^1 \times \mathbb{P}^3$. We use this fact, together with the pure spinor superfield formalism, to study supermultiplets in six dimensions, starting from vector bundles on projective spaces. We classify all multiplets whose derived invariants for the supertranslation algebra form a line bundle over the nilpotence variety; one can think of such multiplets as being those whose holomorphic twists have rank one over Dolbeault forms on spacetime. In addition, we explicitly construct multiplets associated to natural higher-rank equivariant vector bundles, including the tangent and normal bundles as well as their duals. Among the multiplets constructed are the vector multiplet and hypermultiplet, the family of $\mathcal{O}(n)$-multiplets, and the supergravity and gravitino multiplets. Along the way, we tackle various theoretical problems within the pure spinor superfield formalism. In particular, we give some general discussion about the relation of the projective nilpotence variety to multiplets and prove general results on short exact sequences and dualities of sheaves in the context of the pure spinor superfield formalism.
