A cornucopia of AdS 5 vacua
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Springer
Received: May 26, 2020 Accepted: June 22, 2020 Published: July 31, 2020
A cornucopia of AdS5 vacua
a
Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium b Google Research Brandschenkestrasse 110, 8002 Z¨ urich, Switzerland c University of Iceland, Science Institute, Dunhaga 3, 107 Reykjav´ık, Iceland d Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, U.S.A.
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We report on a systematic search for AdS5 vacua corresponding to critical points of the potential in the five-dimensional 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 nonsupersymmetric AdS5 vacua are perturbatively unstable. Many of the new critical points can be found analytically within consistent truncations of the N = 8 supergravity with respect to discrete subgroups of the S(O(6) × GL(2, R)) symmetry of the potential. In particular, we discuss in detail a Z32 -invariant truncation with 10 scalar fields and 15 critical points. We also compute explicitly the scalar potential in a Z22 -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 Z2 -invariant subspace spanned by 22 scalar fields. Keywords: AdS-CFT Correspondence, Gauge-gravity correspondence, Supergravity Models, Superstring Vacua ArXiv ePrint: 2003.03979
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)240
JHEP07(2020)240
Nikolay Bobev,a Thomas Fischbacher,b Fridrik Freyr Gautasona,c and Krzysztof Pilchd
Contents 1 Introduction
1
2 The 10-scalar model 2.1 The consistent truncation 2.2 Critical points
6 6 9 13 13 14 15
4 Critical points from a solvable parametrization 4.1 Solvable parametrization 4.2 The scalar potential and critical points 4.3 Z2 truncations
16 17 18 18
5 Conclusions
21
A Conventions
22
B 14-scalar model B.1 Z2 × Z2 -invariant truncations B.2 Polar parametrization of the coset B.3 Computation of the potential B.4 The critical points B.5 Supplementary material
23 23 24 26 27 27
C Critical points and mass spectra
28
D Scalar mass spectra for the classic vacua
38
1
Introduction
The AdS/CFT correspondence is deeply rooted in string theory and its low-energy supergravity limits. Therefore, it is important to understand fully the landscape of consistent AdS backgrounds in string theory. A fruitful strategy has been to identify a consistent Kaluza-Klein (KK) truncation of a ten- or eleven-dimensional supergr
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