论文标题
与坐标相关的RR场的II型超弦的非交换性和非缔合性
Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field
论文作者
论文摘要
在本文中，我们将考虑在Ramond-Ramond（RR）领域的存在下，由II型超弦的纤维音t二化引起的非交通性，该阶段线性依赖于骨坐标$ X^μ$。 RR场$ C^{αβ} _ $的衍生物是无限的。我们将采用一般的Buscher程序，可以应用于具有坐标相关背景字段的情况。新获得的T二理论的玻色子部分是非本地的。它是在Lagrange乘数$y_μ$跨越的非几何空间中定义的。我们将再次对T二维理论应用广义的Buscher程序，并证明可以挽救原始理论。最后，我们将使用T偶有的转换定律以及原始理论的泊松括号来得出T偶有理论和非社交关系的泊松支架结构。非稳态参数取决于$ x^μ$，$θ^α$和$ \ \barθ^α$，而非缔合参数是一个常数张量，其中包含无穷小的$ c^{αβ}_μ$。
In this paper we will consider noncommutativity that arises from bosonic T-dualization of type II superstring in presence of Ramond-Ramond (RR) field, which linearly depends on the bosonic coordinates $x^μ$. The derivative of the RR field $C^{αβ}_μ$ is infinitesimal. We will employ generalized Buscher procedure that can be applied to cases that have coordinate dependent background fields. Bosonic part of newly obtained T-dual theory is non-local. It is defined in non-geometric space spanned by Lagrange multipliers $y_μ$. We will apply generalized Buscher procedure once more on T-dual theory and prove that original theory can be salvaged. Finally, we will use T-dual transformation laws along with Poisson brackets of original theory to derive Poisson bracket structure of T-dual theory and nonassociativity relation. Noncommutativity parameter depends on the supercoordinates $x^μ$, $θ^α$ and $\barθ^α$, while nonassociativity parameter is a constant tensor containing infinitesimal $C^{αβ}_μ$.
