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arXiv 2003.03979hep-th
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AdS $_5$的聚宝盆

A Cornucopia of AdS$_5$ Vacua

Nikolay Bobev, Thomas Fischbacher, Fridrik Freyr Gautason, Krzysztof Pilch

摘要:

本文报道了在五维$\mathcal{N}=8$ SO(6)规范超引力中系统地寻找与势能临界点相对应的AdS $_5$真空。通过使用Google的TensorFlow机器学习库,我们发现了总共32个关键点,包括5个以前已知的关键点。所有27个新的临界点都是非超对称的。我们计算了所有点的标量涨落的质量谱,发现非超对称的AdS $_5$真空是微扰不稳定的。许多新的临界点可以在$\mathcal{N}=8$超引力相对于势的S(O(6)$\times$ GL(2,$\mathbb{R}$))对称性的离散子群的一致截断中解析地找到。特别地,我们详细讨论了一个具有10个标量场和15个临界点的$\mathbb{Z}_2^3$不变截断。我们还计算明确的标量位在一个$\mathbb{Z}_2^2$不变的扩展,截断到18标量场和再现17的32个临界点的数值搜索。最后,我们表明,作为42个标量场的函数的全势可以分析研究使用所谓的可解参数化。特别地,我们发现所有的临界点都位于由22个标量场构成的$\mathbb{Z}_2$不变子空间中.

英文摘要:

We report on a systematic search for AdS$_5$ vacua corresponding to critical points of the potential in the five-dimensional $\mathcal{N}=8$ SO(6) gauged supergravity. By employing Google's TensorFlow Machine Learning library, we find the total of 32 critical points including 5 previously known ones. All 27 new critical points are non-supersymmetric. We compute the mass spectra of scalar fluctuatons for all points and find that the non-supersymmetric AdS$_5$ vacua are perturbatively unstable. Many of the new critical points can be found analytically within consistent truncations of the $\mathcal{N}=8$ supergravity with respect to discrete subgroups of the S(O(6)$\times$ GL(2,$\mathbb{R}$)) symmetry of the potential. In particular, we discuss in detail a $\mathbb{Z}_2^3$-invariant truncation with 10 scalar fields and 15 critical points. We also compute explicitly the scalar potential in a $\mathbb{Z}_2^2$-invariant extension of that truncation to 18 scalar fields and reproduce 17 of the 32 critical points from the numerical search. Finally, we show that the full potential as a function of 42 scalar fields can be studied analytically using the so-called solvable parametrization. In particular, we find that all critical points lie in a $\mathbb{Z}_2$-invariant subspace spanned by 22 scalar fields.

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