发表机构
Tata Institute of Fundamental Research（塔塔基础研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究德西特空间中的全息性，包括满足狄拉克方程的费米子场，通过路径积分构造Bunch-Davies真空波函数，发现单个体狄拉克场对应边界理论中的一对初级旋量场，并验证了共形Ward恒等式及Yukawa相互作用下的稳健性。
AI 中文摘要
我们研究了德西特空间中全息性的某些方面，涉及关于位于晚期时间边界上的对偶理论的提议[arXiv:astro-ph/0210603v5]，包括满足狄拉克方程的费米子场。我们发现边界附近解的模式具有相等且振荡的衰减，类似于属于德西特空间等距群主序列表示的标量场。我们通过适当地在狄拉克作用中添加边界项，以路径积分形式评估了Bunch-Davies真空的波函数泛函，该泛函以场在类时${\gamma}$-矩阵本征空间上的投影表示。我们通过重现正则形式中计算的真空态下场算符之间的两点函数来验证我们的波函数泛函的路径积分构造。通过适当地将边界源识别为体场投影分量的函数，我们发现体中的单个狄拉克场对应于边界理论中的一对初级旋量场，并证明所得的波函数系数满足共形Ward恒等式。我们通过在相互作用项中的标量场分别属于德西特空间等距群的互补序列和主序列表示的情况下，检查我们的全息映射在添加Yukawa相互作用时的稳健性。
英文摘要
We investigate some aspects of holography in de Sitter space, pertaining to the proposal for the dual theory residing on the late-time boundary [arXiv:astro-ph/0210603v5], including a Fermionic field that satisfies the Dirac equation. The modes of the solutions near the boundary are found to possess equal and oscillatory fall-off, similar to the scalar field belonging to the principal series representation of the isometry group of de Sitter space. We evaluate, by suitably adding a boundary term to the Dirac action, the wavefunctional of the Bunch Davies vacuum in path integral formalism in terms of the projections of the field on the eigenspaces of the time-like $γ$-matrix. We validate our path-integral construction of the wavefunctional by reproducing the two-point function between the field operators in the vacuum state as computed in the canonical formalism. By appropriately identifying the boundary sources in terms of the projected components of the bulk field, we find that a single Dirac field in the bulk corresponds to a pair of primary spinor fields in the boundary theory and show that the resulting wavefunction coefficients satisfy the conformal Ward identities. We check the robustness of our holographic map under the addition of a Yukawa interaction considering the two cases where the scalar field in the interaction term belongs to the complementary series and the principal series representations of the isometry group of de Sitter space respectively.
