New de Sitter solutions in ten dimensions and orientifold singularities
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Springer
Received: March 16, Revised: July 5, Accepted: July 19, Published: August 20,
2020 2020 2020 2020
Clay C´ ordova,a G. Bruno De Lucab,c and Alessandro Tomasiellob,c a
Kadanoff Center for Theoretical Physics & Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, U.S.A. b Dipartimento di Fisica, Universit` a di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy c INFN — Sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
E-mail: [email protected], [email protected], [email protected] Abstract: In previous work, we found ten-dimensional solutions to the supergravity equations of motion with a dS4 factor and O8-planes. We generalize this analysis and obtain other solutions in the same spirit, with an O8+ and an O6− . We examine our original solutions in more detail, focusing in particular on the O8− singularities and on the issues created by their boundary conditions. We also point out some previously known supersymmetric AdS solutions with the same local behavior at their O8− singularity. Keywords: Flux compactifications, Superstring Vacua, Supersymmetry Breaking ArXiv ePrint: 1911.04498
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP08(2020)093
JHEP08(2020)093
New de Sitter solutions in ten dimensions and orientifold singularities
Contents 1 Introduction
1
2 Orientifolds in supergravity
3 5 6 6 7 8 9 10 12
4 A discussion of the O8+ -O8− solutions 4.1 The solutions in detail 4.2 Various versions of the boundary conditions 4.3 Action variation 4.4 Delta-function sources 4.5 Finite masses 4.6 On-shell action 4.7 Summary
14 15 17 18 20 22 24 25
5 Conclusions
26
A AdS4 N = 2 solutions with permissive O8− s
28
1
Introduction
It is a long-standing challenge in string theory to construct solutions with a positive cosmological constant. An essential complication is that within the low-energy supergravity limit there are no-go arguments [1–3] that forbid de Sitter compactifications using only ingredients obeying standard energy conditions. Because of this, any putative de Sitter solution must in some way violate the classical supergravity approximation. For instance, one may make use of corrections to the twoderivative supergravity equations. Alternatively one can try to construct solutions using semiclassical objects, orientifolds, that have negative tension and violate the assumed energy conditions. The latter class of constructions also takes us beyond the supergravity approximation. Close to the orientifolds the curvature and dilaton often become large and stringy corrections again become important.
–1–
JHEP08(2020)093
3 O8+ -O6− solutions 3.1 Review of the O8+ -O8− Ansatz 3.2 Setup 3.2.1 Equations of motion 3.2.2 Flux quantization 3.2.3 O8+ boundary conditions and the cosmological constant 3.3 An analytic AdS starting point 3.4 Numerical solutions
ds210 = e2W ds24 + e−2W (e2λ3 ds2κ3 + dz 2 + e2λ2 ds2S 2 ) ,
(1.1)
where the warp factor W as well as the dilaton and functions λi depend
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