AI 中文总结
研究十维和十一维超引力在卡鲁扎-克莱因背景下的微扰理论，利用E₆(6)例外场论确定场方程，给出希格斯机制细节，通过同伦转移分离场模式，并分析了IIB型超引力在克尔-纽曼AdS₅黑洞周围的模式谱。
AI 中文摘要
我们在一大类卡鲁扎-克莱因背景下发展了十维和十一维超引力的微扰理论，包括如AdS₅×S⁵等常见的反德西特例子以及更一般的流形如黑洞几何。利用具有广义谢尔-施瓦茨假设表征背景的E₆(6)例外场论，确定了在线性化广义微分同胚下规范不变的涨落的一阶场方程。给出了包括自旋-2在内所有场的希格斯机制细节。利用基于同伦转移的机制将场分离为规范不变物理模式和纯规范非物理模式。最后，作为具有高阶规范场背景的首次应用，分析了IIB型超引力在克尔-纽曼AdS₅黑洞周围的十维卡鲁扎-克莱因模式谱的一部分，该黑洞在近视界极限下成为AdS₂和压扁三维球面的纤维积。
英文摘要
We develop the perturbation theory of ten and eleven-dimensional supergravities on a large class of Kaluza-Klein backgrounds including familiar AdS examples such as AdS$_5\times S^5$, but also more general manifolds such as black hole geometries. Employing ${\rm E}_{6(6)}$ exceptional field theory with the backgrounds characterized by a generalized Scherk-Schwarz ansatz, we determine the first order field equations for the fluctuations that are gauge invariant under linearized generalized diffeomorphisms. We then present the details of the Higgs mechanism for all fields including spin-2 for the subset of backgrounds in which higher-form gauge fields vanish. We use a recently established machinery based on homotopy transfer that allows one to separate the fields into gauge invariant physical modes and pure gauge unphysical modes to all orders in perturbation theory. Finally, as a first application for backgrounds with higher-form gauge fields switched on, we analyze part of the spectrum of ten-dimensional Kaluza-Klein modes of type IIB supergravity around a Kerr-Newman AdS$_5$ black hole that in the near horizon limit becomes a fibered product of AdS$_2$ and a squashed three-sphere.
Comments57 pages, 6 figures, 5 tables
