AI 中文总结
本文构建了含共形对偶变换的线性化6维奇异超引力的展开式表述，基于超群$MOSp(16|16)$的超振子实现，定义了相关可观测量，为奇异超引力研究提供了新框架。
AI 中文摘要
我们提供了具有明显超共形对称性的线性化6维奇异超引力的展开式表述，其中包含共形对偶变换。该构造基于亚纯超群$MOSp(16|16)$的超振子实现，该超群包含Howe对偶对$MOSp(8^\text{*}|8)\times SU(2)$。奇异引力子势产生于SU(2)三重态的直积以及由超荷从超荷生成的$OSp(8^\text{*}|8)$的超无迹分级对称二阶超张量的共形对偶对的两个形式中，这提供了$\boldsymbol{\text{psu}(2,2|4)}$伴随表示的类似物。这些势通过相对Chevalley-Eilenberg上同调由手征和反手征Weyl零形式的共形对偶对提供源，这些零形式取值于扩展超单态的$SO(1,1)\times Spin(1,5)\times USp(8)$协变单态限制，即$MOSp(8^\text{*}|8)$的无限维SU(2)不变埃尔米特左模，包含与不同边界条件相关的各种不可约表示，包括可酉化的奇异超引力多重态。两个自然的二次可观测量为：i) 由手征Weyl零形式及其对偶构成的壳上闭合零形式，类似于4维Vasiliev系统内部扭量Z空间上第二陈类的壳上值；ii) 由两个形式势的共形对偶对构成的离壳拓扑六形式，在壳上约化为超庞加莱背景下手征两点函数的生成函数。
英文摘要
We provide an unfolded formulation of linearised 6D exotic supergravity with manifest superconformal symmetry including conformal duality transformations. The construction is based on a superoscillator realisation of the metaplectic supergroup $MOSp(16|16)$ containing the Howe dual pair $MOSp(8^\ast|8)\times SU(2)$. Exotic graviton potentials arise in conformally dual pairs of two-forms in direct products of $SU(2)$-triplets and supertraceless graded-symmetric rank-two supertensors of $OSp(8^\ast|8)$ generated from a hypercharge by the supercharges, providing an analogue of the adjoint representation of $\mathfrak{psu}(2,2|4)$. The potentials are sourced via relative Chevalley-Eilenberg cocycles by a conformally dual pair of chiral and anti-chiral Weyl zero-forms valued in $SO(1,1)\times Spin(1,5)\times USp(8)$-covariant monomorphic restrictions of an extended supersingleton, i.e., an infinite-dimensional $SU(2)$-invariant Hermitian left-module of $MOSp(8^\ast|8)$ containing various irreps associated with different boundary conditions, including the unitarizable exotic supergravity multiplet. Two natural quadratic observables are i) an on-shell closed zero-form built from the chiral Weyl zero-form and its dual, akin to the on-shell value of the second Chern class on the internal twistor $Z$-space of 4D Vasiliev systems; and ii) an off-shell topological six-form built from the conformally dual pair of two-form potentials, reducing on-shell to a generating function for chiral two-point functions in super-Poincaré backgrounds.
Comments75 pages
