论文标题
有限$ W $ -SUPERALGEBRAS和二次超超对称性
Finite $W$-superalgebras and quadratic spacetime supersymmetries
论文作者
论文摘要
我们认为，在汉密尔顿减少的限制下，超级甲壳虫在超级甲壳虫中产生有限的$ W $ -SUPERALGEBRA，这为二次二级超级级别的超级甲壳虫提供了候选。这些具有未呈现的玻色谐对称代数（甚至是发电机），由费米子扇区（超对称发生器）分级，其抗强制支架在均匀的发生器中是二次的。我们在古典（Poisson支架）水平上分析了$ gl（m | n）$或$ osp（m | 2n）$的几个谎言超级船的减少，并建立了量子（lie barket）等效物。还考虑了纯粹的骨扩展。作为一个特殊情况，我们恢复了最近确定的二次超符合代数，某些统一的不可约定的无质量表示（四个维度）是“零步”的多重组，而没有伴随的超级零件。研究的其他案例包括带有矢量奇数发生器的六维二次超符合代数，以及具有未呈$ osp（1 | 2n）$ singleton sopersymmememmetry的变体二次超级级代数，以及旋转增压的三重态。
We consider Lie superalgebras under constraints of Hamiltonian reduction, yielding finite $W$-superalgebras which provide candidates for quadratic spacetime superalgebras. These have an undeformed bosonic symmetry algebra (even generators) graded by a fermionic sector (supersymmetry generators) with anticommutator brackets which are quadratic in the even generators. We analyze the reduction of several Lie superalgebras of type $gl(M|N)$ or $osp(M|2N)$ at the classical (Poisson bracket) level, and also establish their quantum (Lie bracket) equivalents. Purely bosonic extensions are also considered. As a special case we recover a recently identified quadratic superconformal algebra, certain of whose unitary irreducible massless representations (in four dimensions) are "zero-step" multiplets, with no attendant superpartners. Other cases studied include a six dimensional quadratic superconformal algebra with vectorial odd generators, and a variant quadratic superalgebra with undeformed $osp(1|2N)$ singleton supersymmetry, and a triplet of spinorial supercharges.
