论文标题

$ \ MATHCAL n = 2 $ ads $ _4 $ SUPERGRAVITY,全息和病房身份

$\mathcal N=2$ AdS$_4$ supergravity, holography and Ward identities

论文作者

Andrianopoli, L., Cerchiai, B. L., Matrecano, R., Miskovic, O., Noris, R., Olea, R., Ravera, L., Trigiante, M.

论文摘要

我们详细开发了$ \ Mathcal {n} = 2 $ Pure Ad Supergravity模型的全息框架,包括四个维度,包括Fermionic Fields的所有贡献并采用Fefferman-Graham参数化。我们在一阶形式主义中工作,即使只有一部分被实现为边界上的对称性,而其余部分则具有非线性实现。我们的研究概括了在先前文献中提出的结果,其中包括对块状场上量规条件的一般讨论,这些条件在边界处产生渐近对称性。我们构建相应的超符号电流,并表明当施加大量运动时,它们满足了相关的病房身份。 全息设置的一致性要求超级ads曲率在边界上消失。这尤其确定了边界理论的超轴张量的表达,该张量通过包括gravitini biLinears来概括了标准重力的纯粹的骨schouten张量。同样,也适用于超级量张量的超级球员。此外,超级物品的消失对三维边界综合场理论的来源产生了一般的约束,并要求超级张量的超对称部件与重力固定词成比例。

We develop in detail the holographic framework for an $\mathcal{N}=2$ pure AdS supergravity model in four dimensions, including all the contributions from the fermionic fields and adopting the Fefferman-Graham parametrization. We work in the first order formalism, where the full superconformal structure can be kept manifest in principle, even if only a part of it is realized as a symmetry on the boundary, while the remainder has a non-linear realization. Our study generalizes the results presented in antecedent literature and includes a general discussion of the gauge-fixing conditions on the bulk fields which yield the asymptotic symmetries at the boundary. We construct the corresponding superconformal currents and show that they satisfy the related Ward identities when the bulk equations of motion are imposed. Consistency of the holographic setup requires the super-AdS curvatures to vanish at the boundary. This determines, in particular, the expression of the super-Schouten tensor of the boundary theory, which generalizes the purely bosonic Schouten tensor of standard gravity by including gravitini bilinears. The same applies to the superpartner of the super-Schouten tensor, the conformino. Furthermore, the vanishing of the supertorsion poses general constraints on the sources of the three-dimensional boundary conformal field theory and requires that the super-Schouten tensor is endowed with an antisymmetric part proportional to a gravitino-squared term.

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