[论文解读] Classical and Quantum Nonlocal Supergravity

Stefano Giaccari, Leonardo Modesto|arXiv (Cornell University)|May 12, 2016

Cosmology and Gravitation Theories参考文献 58被引用 7

一句话总结

本文使用超空间形式化方法，构建了弱非局域四维超引力的N=1超对称推广，确保了树幅微扰幺正性和无鬼态。该理论是超重整化可重正化的，其谱与局域超引力相同，且通过“超杀手”算符实现了量子层面的有限性，尽管非局域性并未消除时空奇点。

ABSTRACT

We derive the N=1 supersymmetric extension for a class of weakly nonlocal four dimensional gravitational theories.The construction is explicitly done in the superspace and the tree-level perturbative unitarity is explicitly proved both in the superfield formalism and in field components. For the minimal nonlocal supergravity the spectrum is the same as in the local theory and in particular it is ghost-free. The supersymmetric extension of the super-renormalizable Starobinsky theory and of two alternative massive nonlocal supergravities are found as straightforward applications of the formalism. Power-counting arguments ensure super-renormalizability with milder requirement for the asymptotic behavior of form factors than in ordinary nonlocal gravity. The most noteworthy result, common to ordinary supergravity, is the absence of quantum corrections to the cosmological constant in any regularization procedure. We cannot exclude the usual one-loop quadratic divergences. However, local vertices in the superfields, not undergoing renormalization, can be introduced to cancel out such divergences. Therefore, quantum finiteness is certainly achieved in dimensional regularization and most likely also in the cut-off regularization scheme. We also discuss the n-point scattering amplitudes making use of a general field redefinition theorem implemented in the superspace. Finally, we show that all the exact solutions of the local supergravity in vacuum are solutions of the nonlocal one too. In particular, we have the usual Schwarzschild singularity. We infer that the weak nonlocality, even in the presence of minimal supersymmetry, is not sufficient to solve the spacetime singularities issue, although the theory is finite at quantum level.

研究动机与目标

• 将弱非局域、无鬼态引力推广至保持幺正性和有限性的超对称框架。
• 确保谱与局域N=1超引力一致，避免引入非物理态。
• 通过维度正规化和截断正规化中的‘超杀手’算符，证明量子有限性。
• 研究非局域性是否能解决超引力中的时空奇点问题。
• 推广场重新定义定理，证明树幅n点散射振幅与局域超引力等价。

提出的方法

• 在超空间中构造包含d’Alembert算子整函数的非局域超引力作用量。
• 使用超场形式化，显式保持非壳N=1超对称性。
• 推导分量二次作用量，显示动能项受exp[H(□)]修正，其中H为整函数。
• 应用计数论证，确立超重整化可重正化性，并降低UV形式因子的要求。
• 引入局部四次超场算符（‘超杀手’项）以抵消一环发散。
• 推广场重新定义定理，证明树幅n点振幅与局域超引力等价。

实验结果

研究问题

• RQ1 能否在超空间中构造出具有显式非壳超对称性的弱非局域、无鬼态超引力？
• RQ2 该非局域推广是否保持与局域N=1超引力相同的物理谱？
• RQ3 能否通过局部反项在维度正规化和截断正规化中实现量子有限性？
• RQ4 非局域性是否足以消除经典时空奇点（如史瓦西奇点）？
• RQ5 该非局域理论中的树幅散射振幅是否与局域超引力完全相同？

主要发现

• 在超空间中构建了非局域超引力的N=1超对称推广，保持了非壳超对称性和树幅幺正性。
• 物理谱与局域N=1超引力完全相同，由引力子、引力微子和辅助场构成，无鬼态。
• 该理论为超重整化可重正化，仅存在一环发散，且通过维度正规化中的‘超杀手’算符可实现量子有限性。
• 即使在截断正规化下，通过增加一个额外局部算符以抵消爱因斯坦-希尔伯特发散，有限性也极有可能实现。
• 所有树幅散射振幅均与局域爱因斯坦超引力完全相同，确认了经典微扰层面的局域性。
• 该非局域理论与局域超引力具有相同的精确真空解，包括奇异的史瓦西度规，表明弱非局域性无法消除时空奇点。