标题： 利用 exceptional field 理论的 AdS 真空的三次和高阶超引力耦合 显示英文标题

标题： Cubic and higher-order supergravity couplings for AdS vacua using Exceptional Field Theory

摘要： 我们展示了如何利用例外场论来有效地计算可以从极大规范超引力通过一致约化提升到10/11维的真空的所有Kaluza-Klein模式的$n$点耦合。通过 AdS/CFT 对偶，这些耦合编码了全息共形场论的$n$点函数。我们的方法表明这些$n$点耦合由约化最大对称点标量谐波的$n$点不变量控制，从而我们可以证明对于约化任意真空，无穷多个$n$点耦合都为零，尽管它们可能被真空剩余对称群所允许。 这甚至为弦论和M理论的极大超对称AdS$_5 \times S^5$、AdS$_4 \times S^7$和AdS$_7 \times S^4$真空提供了新的结果，我们证明了关于$n$-点极值和接近极值耦合消失的老猜想。 特别关注于五维规范超引力真空的三次耦合，我们推导出了一致截断内任意真空的这些耦合的显式通用公式。 我们用它来计算已知和新的涉及自旋-0、自旋-1、自旋-2的耦合，针对IIB弦论的AdS$_5 \times S^5$真空。 显示英文摘要

摘要： We show how to use Exceptional Field Theory to efficiently compute $n$-point couplings of all Kaluza-Klein modes for vacua that can be uplifted from maximal gauged supergravities to 10/11 dimensions via a consistent truncation. Via the AdS/CFT correspondence, these couplings encode the $n$-point functions of holographic conformal fields theories. Our methods show that these $n$-point couplings are controlled by the $n$-point invariant of scalar harmonics of the maximally symmetric point of the truncation, allowing us to show that infinitely-many $n$-point couplings vanish for any vacua of the truncation, even though they may be allowed by the remnant symmetry group of the vacua. This gives new results even for the maximally supersymmetric AdS$_5 \times S^5$, AdS$_4 \times S^7$ and AdS$_7 \times S^4$ vacua of string and M-theory, where we prove old conjectures about the vanishing of $n$-point extremal and near-extremal couplings. Focusing in particular on cubic couplings for vacua of 5-dimensional gauged supergravity, we derive explicit universal formulae encoding these couplings for any vacuum within a consistent truncation. We use this to compute known and new couplings involving spin-0, spin-1, spin-2 for the AdS$_5 \times S^5$ vacuum of IIB string theory.