arXiv 1707.034112017-07-11hep-th

$D=2+2$中的规范超引力

Gauge supergravity in $D=2+2$

Leonardo Castellani

备注：: LaTeX, 10 pages
DOI：: 10.1007/JHEP10(2017)062

摘要：

本文给出了手征$N=(1,0)$超引力在$2+2$维中的作用量。该理论的领域被组织成一个$OSp(1|4)$连接超矩阵，并由通常的Vierbein $V^a$，自旋连接$ω^{ab}$和Majorana引力子$ψ$给出。类似于用于$D=10+2$规范超引力的构造，作用量由$\int STr ({\bf R}^2 {\bf Γ})$给出，其中${\bf R}$是$OSp(1|4)$曲率超矩阵的二形式，而${\bf Γ}$是包含$γ_5$的常数超矩阵。它与$D=2+2$超引力的麦克道尔-曼苏尔作用量类似，但不完全相同。常数超矩阵将$OSp(1|4)$规范不变性分解为一个子代数$OSp(1|2) \oplus Sp(2)$，其中包含一个Majorana-Weyl超荷。因此，$OSp(1|4)$规范超对称性的一半得以保留。对于$OSp(1|2)$，规范场是$ω^{ab}$的自对偶部分和$ψ$的Weyl投影;对于$Sp(2)$，规范场是$ω^{ab}$的反自对偶部分。超对称变换，作为规范超代数的一部分，闭壳。自旋联系上的自对偶条件可以一致地施加，并且由此产生的“投影”作用量是$OSp(1|2)$规范不变量。

英文摘要：

We present an action for chiral $N=(1,0)$ supergravity in $2+2$ dimensions. The fields of the theory are organized into an $OSp(1|4)$ connection supermatrix, and are given by the usual vierbein $V^a$, spin connection $ω^{ab}$, and Majorana gravitino $ψ$. In analogy with a construction used for $D=10+2$ gauge supergravity, the action is given by $\int STr ({\bf R}^2 {\bf Γ})$, where ${\bf R}$ is the $OSp(1|4)$ curvature supermatrix two-form, and ${\bf Γ}$ a constant supermatrix containing $γ_5$. It is similar, but not identical to the MacDowell-Mansouri action for $D=2+2$ supergravity. The constant supermatrix breaks $OSp(1|4)$ gauge invariance to a subalgebra $OSp(1|2) \oplus Sp(2)$, including a Majorana-Weyl supercharge. Thus half of the $OSp(1|4)$ gauge supersymmetry survives. The gauge fields are the selfdual part of $ω^{ab}$ and the Weyl projection of $ψ$ for $OSp(1|2)$, and the antiselfdual part of $ω^{ab}$ for $Sp(2)$. Supersymmetry transformations, being part of a gauge superalgebra, close off-shell. The selfduality condition on the spin connection can be consistently imposed, and the resulting "projected" action is $OSp(1|2)$ gauge invariant.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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