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arXiv 2010.02119hep-thgr-qc
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$\mathcal N=2$ AdS $_4$超引力、全息和沃德恒等式

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

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

摘要:

我们详细地发展了一个四维$\mathcal{N}=2$纯AdS超引力模型的全息框架,包括了所有来自费米子场的贡献,并采用了Festhiman-Graham参数化.我们工作在一阶形式主义,在那里的完整的超共形结构可以保持明显的原则,即使只有一部分是实现为边界上的对称,而其余的非线性实现。我们的研究概括了先前文献中提出的结果,并包括一个一般性的讨论的规范固定条件的散装领域产生的渐近对称性的边界。我们构造了相应的超共形流,并证明了当施加体运动方程时,它们满足相关的沃德恒等式。全息设置的一致性要求超AdS曲率在边界处消失。这特别决定了边界理论的超斯考滕张量的表达式,它通过包含gravitini双线性来推广标准引力的纯玻色子斯考滕张量。这同样适用于超斯考滕张量的超伴子--共形伴子。此外,超挠的消失对三维边界共形场论的源提出了一般的约束,并要求超斯考滕张量被赋予与引力平方项成比例的反对称部分。

英文摘要:

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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