论文标题
共形$（p，q）$ supergeometries二维
Conformal $(p,q)$ supergeometries in two dimensions
论文作者
论文摘要
我们为保形$（p，q）$ supergravity提出了一个超空间公式，作为超级符号组$ \ mathsf {osp} _0（p | 2; {\ mathbb r}）\ times \ times \ mathsf {osp} {osp} _0（q | 2 | 2 | 2;在某些局部对称性的脱盖后，该保质超空间被证明可以减少到合成平坦的$ \ mathsf {so}（p）\ times \ times \ times \ mathsf {so}（q）$ superspace具有以下属性：（i）其结构组是Lorentz Group and $ \ Mathsf的直接产品\ Mathsf {so}（q）$; （ii）残留的局部规模对称性是通过具有不受约束的实际参数的超韦尔变换来实现的。作为形式主义的应用，我们将$ {\ cal n} $ - 扩展广告超空间作为最大对称的超级几何，在$ p = q \ equiv \ equiv \ cal n $ case中。如果至少一个参数$ p $或$ q $是偶数，则替代超级符号组，因此存在保形超级空间。特别是，如果$ p = 2n $，那么超级符号组的可能选择是$ \ mathsf {su}（1,1 | n）\ times \ times \ mathsf {osp} _0（q | 2; {\ m缩br r}）$ \ Mathsf {osp} _0（q | 2; {\ Mathbb r}）$，当$ n = 2 $时。通常，共形超空间配方与超组$ g = g_l \ times g_r $相关联，其中简单的超级组$ g_l $和$ g_r $可以是任何扩展的超级构造群体，这些群体由Günaydin，Sierra和Townsend分类。脱盖相应的共形超空间会导致一个固定的平面$ h_l \ times h_r $ superspace，其中$ h_l $（$ h_r $）是$ r $ -smmetry子组为$ g_l $（$ g_r $）。此外，对于$ p，q \ leq 2 $案例，我们提出了复合主要多重组，从而生成了弗拉德金 - tseytlin术语的高斯 - 骨网不变和超对称扩展。
We propose a superspace formulation for conformal $(p,q)$ supergravity in two dimensions as a gauge theory of the superconformal group $\mathsf{OSp}_0 (p|2; {\mathbb R} ) \times \mathsf{OSp}_0 (q|2; {\mathbb R} )$ with a flat connection. Upon degauging of certain local symmetries, this conformal superspace is shown to reduce to a conformally flat $\mathsf{SO}(p) \times \mathsf{SO}(q)$ superspace with the following properties: (i) its structure group is a direct product of the Lorentz group and $\mathsf{SO}(p) \times \mathsf{SO}(q)$; and (ii) the residual local scale symmetry is realised by super-Weyl transformations with an unconstrained real parameter. As an application of the formalism, we describe ${\cal N}$-extended AdS superspace as a maximally symmetric supergeometry in the $p=q \equiv \cal N$ case. If at least one of the parameters $p$ or $q$ is even, alternative superconformal groups and, thus, conformal superspaces exist. In particular, if $p = 2n$, a possible choice of the superconformal group is $\mathsf{SU}(1,1|n) \times \mathsf{OSp}_0 (q|2; {\mathbb R} )$, for $n \neq 2$, and $\mathsf{PSU}(1,1|2) \times \mathsf{OSp}_0 (q|2; {\mathbb R} )$, when $n=2$. In general, a conformal superspace formulation is associated with a supergroup $ G = G_L \times G_R$, where the simple supergroups $G_L$ and $G_R$ can be any of the extended superconformal groups, which were classified by Günaydin, Sierra and Townsend. Degauging the corresponding conformal superspace leads to a conformally flat $H_L \times H_R$ superspace, where $H_L $ ($H_R$) is the $R$-symmetry subgroup of $G_L$ ($G_R$). Additionally, for the $p,q \leq 2$ cases we propose composite primary multiplets which generate the Gauss-Bonnet invariant and supersymmetric extensions of the Fradkin-Tseytlin term.
