论文标题
手性，定义Lie-kac超级代数的连接和曲率的新钥匙
Chirality, a new key for the definition of the connection and curvature of a Lie-Kac super-algebra
论文作者
论文摘要
提出了对Lie-Kac Superalgebra（例如SU（M/N）的情况，就普通的复杂函数和差异而言，对Lie代数连接或Yang-Mills字段的自然概括。使用手性$χ$定义了SuperAlgebra的超丝：$ str（...）= tr（χ...）$，我们构造了协变量差异：$ d =χ（d + a） +φ$，其中a是标准的lie-subalgebra连接1型和$φ$ a scalar Field Field在奇数模块中的价值。尽管$φ$是标量，但带有$（χa）$的$φ$ antymutes，因为$χ$ antymutes与$φ$中的奇数发电机。因此，曲率$ f = dd $是一个超级值的线性图，它尊重比安奇的身份，并正确定义了与通用的谎言超级级别级别结构兼容的手性平行传输。
A natural generalization of a Lie algebra connection, or Yang-Mills field, to the case of a Lie-Kac superalgebra, for example SU(m/n), just in terms of ordinary complex functions and differentials, is proposed. Using the chirality $χ$ which defines the supertrace of the superalgebra: $STr(...) = Tr (χ...)$, we construct a covariant differential: $D = χ(d + A) + Φ$, where A is the standard even Lie-subalgebra connection 1-form and $Φ$ a scalar field valued in the odd module. Despite the fact that $Φ$ is a scalar, $Φ$ anticommutes with $(χA)$ because $χ$ anticommutes with the odd generators hidden in $Φ$. Hence the curvature $F = DD$ is a superalgebra-valued linear map which respects the Bianchi identity and correctly defines a chiral parallel transport compatible with a generic Lie superalgebra structure.
