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We study flux compactifications of 10d type II supergravities to 4d Minkowski space-time, supported by parallel orientifold Op-planes with 3 $\leq$ p $\leq$ 8.
K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux
1999
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J. M. Maldacena and C. Nuñez, Supergravity description of field theories on curved manifolds and a no go theorem
2001
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S. B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications
2002
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S. Kachru, M. B. Schulz, P. K. Tripathy and S. P. Trivedi, New supersymmetric string compactifications
2003
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O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization
2005
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J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications
2005
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M. Graña, Flux compactifications in string theory: A Comprehensive review
2006
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M. Graña, R. Minasian, M. Petrini and A. Tomasiello, A Scan for new N=1 vacua on twisted tori
2007
Cited alongside, same era.
2007
Cited alongside, same era.
2010
Cited alongside, same era.
We define the square of the q q -form A q A_{q} as | A q | 2 = A m 1 … m q A m 1 … m p / q ! |A_{q}|^{2}=A_{m_{1}\ldots m_{q}}A^{m_{1}\ldots m_{p}}/q! , the sign ε p = ( − 1 ) [ 9 − p 2 ] + p + 1 \varepsilon_{p}=(-1)^{\left[\frac{9-p}{2}\right]+p+1} , and sources are localized in transverse directions through T 10 = 2 κ 10 2 | g ⊥ | ( p + 1 ) T p ( ∑ O p 2 p − 5 δ ( ⊥ ) − ∑ D p δ ( ⊥ ) ) T_{10}=\tfrac{2\kappa_{10}^{2}}{\sqrt{|g_{\bot}|}}\,(p+1)T_{p}\Big(\sum_{O_{p}}\!2^{p-5}\delta(\bot)-\sum_{D_{p}}\!\delta(\bot)\Big) . We consider BPS sources where tension and charge are related as T p = μ p T_{p}=\mu_{p} , and without world-volume flux
Cited in the paper.
Proving that F 4 − p = 0 F_{4-p}=0 actually requires another combination of e.o.m. worked-out in Andriot:2016xvq , namely the one that allows to conclude on the no-go for p = 7 , 8 p=7,8
Cited in the paper.
The non-zero fluxes may also enter the F 10 − p F_{10-p} BI through H ∧ F 8 − p H\wedge F_{8-p} , but this quantity vanishes as it should, given its number of transverse components
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| f a | | | 2 b ⊥ c ⊥ = δ a b 2 δ e f δ g h f a | | f b | | e ⊥ g ⊥ = f ⊥ h ⊥ ∑ a | | | ( d e a | | ) | ⊥ | 2 |f^{a_{||}}{}_{b_{\bot}c_{\bot}}\!|^{2}\!=\!\tfrac{\delta_{ab}}{2}\delta^{ef}\!\delta^{gh}\!f^{a_{||}}{}_{e_{\bot}g_{\bot}}\!f^{b_{||}}{}_{f_{\bot}h_{\bot}}\!\!=\!\!\sum_{a_{||}}\!|(\textrm{d}e^{a_{||}})|_{\bot}|^{2}
Cited in the paper.
The internal manifold and transverse subspace having no boundary, one has f ~ a | | a | | d ⊥ = 0 \tilde{f}^{a_{||}}{}_{a_{||}d_{\bot}}=0 . One then shows that d vol ~ | | = e − A ( p − 3 ) ∑ a | | ∗ 6 ( e a | | ∧ ∗ ⊥ ( d e a | | ) | ⊥ ) \textrm{d}\widetilde{\mbox{vol}}_{||}=e^{-A(p-3)}\sum_{a_{||}}*_{6}\left(e^{a_{||}}\wedge*_{\bot}(\textrm{d}e^{a_{||}})|_{\bot}\right) , allowing to prove that F 8 − p F_{8-p} in ( 8
Cited in the paper.
2013
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D. Geissbühler, D. Marques, C. Nuñez and V. Penas, Exploring Double Field Theory
2013
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F. F. Gautason, M. Schillo, T. Van Riet and M. Williams, Remarks on scale separation in flux vacua
2016
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D. Andriot, New supersymmetric vacua on solvmanifolds
2016
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D. Andriot and J. Blåbäck, Refining the boundaries of the classical de Sitter landscape
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2017
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