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Journal articles on the topic 'Supergravity Vacua'

Author: Grafiati

Published: 14 March 2023

Last updated: 31 July 2025

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1

Taylor-Robinson, Marika M. "Semiclassical stability of supergravity vacua." Physical Review D 55, no. 8 (1997): 4822–38. http://dx.doi.org/10.1103/physrevd.55.4822.

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2

Gómez-Reino, Marta, and Claudio A. Scrucca. "Metastable supergravity vacua withFandDsupersymmetry breaking." Journal of High Energy Physics 2007, no. 08 (2007): 091. http://dx.doi.org/10.1088/1126-6708/2007/08/091.

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3

Cowdall, P. M., and P. K. Townsend. "Gauged supergravity vacua from intersecting branes." Physics Letters B 429, no. 3-4 (1998): 281–88. http://dx.doi.org/10.1016/s0370-2693(98)00445-6.

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4

Antoniadis, I., C. Bachas, and A. Sagnotti. "Gauged supergravity vacua in string theory." Physics Letters B 235, no. 3-4 (1990): 255–60. http://dx.doi.org/10.1016/0370-2693(90)91960-j.

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5

HU, SEN, ZHI HU, and RUORAN ZHANG. "GENERALIZED RICCI FLOW AND SUPERGRAVITY VACUUM SOLUTIONS." International Journal of Modern Physics A 25, no. 12 (2010): 2535–49. http://dx.doi.org/10.1142/s0217751x10048238.

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We first give a proof that the supersymmetric configurations satisfy the equations of motion for type II supergravity. In flux compactifications, the string vacua preserving N = 2 supersymmetry are the twisted generalized Calabi–Yau manifold. The modulus space of the string vacua can be constructed. We discuss the generalized Dirac operator which adds a torsional term to the ordinary Dirac operator and compute its index by the path integral method. Via the variation of the action of supergravity one can introduce the generalized Ricci flow equations. We consider deforming the manifold with the

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6

Behrndt, Klaus, and Swapna Mahapatra. "De Sitter vacua fromN=2 gauged supergravity." Journal of High Energy Physics 2004, no. 01 (2004): 068. http://dx.doi.org/10.1088/1126-6708/2004/01/068.

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7

Freedman, Daniel Z., and Boris Körs. "Kähler anomalies in supergravity and flux vacua." Journal of High Energy Physics 2006, no. 11 (2006): 067. http://dx.doi.org/10.1088/1126-6708/2006/11/067.

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8

Inverso, Gianluca. "Vacua and Gaugings of MaximalD= 4 Supergravity." Journal of Physics: Conference Series 383 (October 1, 2012): 012001. http://dx.doi.org/10.1088/1742-6596/383/1/012001.

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9

Kehagias, A. "De Sitter vacua in simple extended supergravity." Fortschritte der Physik 57, no. 5-7 (2009): 606–10. http://dx.doi.org/10.1002/prop.200900014.

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10

Malek, Emanuel, and Valentí Vall Camell. "Consistent truncations around half-maximal AdS₅ vacua of 11-dimensional supergravity." Classical and Quantum Gravity 39, no. 7 (2022): 075026. http://dx.doi.org/10.1088/1361-6382/ac566a.

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Abstract We use exceptional field theory to systematically study all possible consistent truncations around any M-theory half-maximal vacua of the warped product form AdS5 × M 3 × S 2 × S 1, with M 3 a three-dimensional manifold. We show that, for any of these vacua, only truncations with at most three vector multiplets are consistent. Furthermore, the possible gaugings are restricted to be either SU(2) × U(1) or ISO(3) × U(1) where, in the first case, the U(1) factor can have different embeddings inside the global symmetry group SO(5, n), where n ⩽ 3 equals the number of vector multiplets. Th

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11

Chatrabhuti, Auttakit, and Parinya Karndumri. "Vacua of N = 10 three-dimensional gauged supergravity." Classical and Quantum Gravity 28, no. 12 (2011): 125027. http://dx.doi.org/10.1088/0264-9381/28/12/125027.

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12

Gómez-Reino, Marta, and Claudio A. Scrucca. "Locally stable non-supersymmetric Minkowski vacua in supergravity." Journal of High Energy Physics 2006, no. 05 (2006): 015. http://dx.doi.org/10.1088/1126-6708/2006/05/015.

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13

Fr, Pietro, Mario Trigiante, and Antoine Van Proeyen. "2 supergravity models with stable de Sitter vacua." Classical and Quantum Gravity 20, no. 12 (2003): S487—S493. http://dx.doi.org/10.1088/0264-9381/20/12/314.

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14

Serone, Marco, and Alexander Westphal. "Moduli stabilization in meta-stable heterotic supergravity vacua." Journal of High Energy Physics 2007, no. 08 (2007): 080. http://dx.doi.org/10.1088/1126-6708/2007/08/080.

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15

Cvetič, Mirjam, Stephen Griffies, and Soo-Jong Rey. "Non-perturbative stability of supergravity and superstring vacua." Nuclear Physics B 389, no. 1 (1993): 3–24. http://dx.doi.org/10.1016/0550-3213(93)90283-u.

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16

Khavaev, Alexei, Krzysztof Pilch, and Nicholas P. Warner. "New vacua of gauged supergravity in five dimensions." Physics Letters B 487, no. 1-2 (2000): 14–21. http://dx.doi.org/10.1016/s0370-2693(00)00795-4.

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17

McORIST, JOCK. "THE REVIVAL OF (0, 2) SIGMA MODELS." International Journal of Modern Physics A 26, no. 01 (2011): 1–41. http://dx.doi.org/10.1142/s0217751x11051366.

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Compactifications of the heterotic string are a viable route to phenomenologically realistic vacua and interesting new mathematics. While supergravity aspects of heterotic compactifications are largely well-understood their worldsheet description remains largely unexplored. We review recent work in developing linear sigma model techniques aimed at elucidating the underlying worldsheet description.

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18

Kerimo, J., James T. Liu, H. Lü, and C. N. Pope. "Variant = (1,1) supergravity and (Minkowski) 4 × S 2 vacua." Classical and Quantum Gravity 21, no. 13 (2004): 3287–300. http://dx.doi.org/10.1088/0264-9381/21/13/011.

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19

Baer, Howard, Michal Brhlik, and Diego Castaño. "Constraints on the minimal supergravity model from nonstandard vacua." Physical Review D 54, no. 11 (1996): 6944–56. http://dx.doi.org/10.1103/physrevd.54.6944.

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20

DallʼAgata, G., and G. Inverso. "On the vacua of gauged supergravity in 4 dimensions." Nuclear Physics B 859, no. 1 (2012): 70–95. http://dx.doi.org/10.1016/j.nuclphysb.2012.01.023.

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21

BURINSKII, ALEXANDER. "CASIMIR ENERGY AND VACUA FOR SUPERCONDUCTING BALL IN SUPERGRAVITY." International Journal of Modern Physics A 17, no. 06n07 (2002): 920–25. http://dx.doi.org/10.1142/s0217751x02010315.

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Casimir energy for solid conducting ball is considered on the base of some finite models. One model is physical and built of a battery of parallel metallic plates. Two finite models are based on the Higgs model of superconductivity. One of them is supersymmetric and based on the Witten field model for superconducting strings. Treatment shows that contribution of Casimir energy can be very essential for superdence state in the neutron stars and nuclear matter.

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22

Froggatt, C. D., R. Nevzorov, H. B. Nielsen, and A. W. Thomas. "Predicting the SUSY breaking scale in SUGRA models with degenerate vacua." International Journal of Modern Physics A 35, no. 01 (2020): 2050007. http://dx.doi.org/10.1142/s0217751x20500074.

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In [Formula: see text] supergravity, the scalar potential may have supersymmetric (SUSY) and nonsupersymmetric Minkowski vacua (associated with supersymmetric and physical phases) with vanishing energy density. In the supersymmetric Minkowski (second) phase, some breakdown of SUSY may be induced by nonperturbative effects in the observable sector that give rise to a tiny positive vacuum energy density. Postulating the exact degeneracy of the physical and second vacua as well as assuming that at high energies the couplings in both phases are almost identical, one can estimate the dark energy de

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23

Fr$eacute$, Pietro, Mario Trigiante, and Antoine Van Proeyen. "Stable de Sitter vacua from $\Script N$ $equal$ 2 supergravity." Classical and Quantum Gravity 19, no. 15 (2002): 4167–93. http://dx.doi.org/10.1088/0264-9381/19/15/319.

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24

Cosemans, Bert, and Geert Smet. "Stable de Sitter vacua in N = 2, D = 5 supergravity." Classical and Quantum Gravity 22, no. 12 (2005): 2359–80. http://dx.doi.org/10.1088/0264-9381/22/12/004.

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25

Chamseddine, Ali H., and Mikhail S. Volkov. "Non-Abelian vacua in D = 5, N = 4 gauged supergravity." Journal of High Energy Physics 2001, no. 04 (2001): 023. http://dx.doi.org/10.1088/1126-6708/2001/04/023.

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26

Singh, Harvendra. "New supersymmetric vacua for D=4, N=4 gauged supergravity." Physics Letters B 429, no. 3-4 (1998): 304–12. http://dx.doi.org/10.1016/s0370-2693(98)00463-8.

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27

Cao, Zhen-Bin. "Supersymmetric AdS 4 vacua in ${\mathscr{N}}=3$ gauged supergravity." Chinese Physics C 42, no. 5 (2018): 053104. http://dx.doi.org/10.1088/1674-1137/42/5/053104.

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28

Malek, Emanuel, and Henning Samtleben. "Ten-dimensional origin of Minkowski vacua in N=8 supergravity." Physics Letters B 776 (January 2018): 64–71. http://dx.doi.org/10.1016/j.physletb.2017.11.011.

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29

Cvetič, Mirjam, and Donam Youm. "BPS saturated dyonic black holes of N = 8 supergravity vacua." Nuclear Physics B - Proceedings Supplements 46, no. 1-3 (1996): 56–66. http://dx.doi.org/10.1016/0920-5632(96)00007-2.

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30

Riet, Thomas Van. "No accelerating scaling cosmologies at string tree level?" Journal of Cosmology and Astroparticle Physics 2024, no. 01 (2024): 055. http://dx.doi.org/10.1088/1475-7516/2024/01/055.

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Abstract We investigate the scalar potential in the parametric regime of string moduli space where string loops and higher derivative corrections to 10d supergravity can be ignored and where the fields are rolling down exponential slopes leading to powerlaw FLRW cosmologies, a.k.a. scaling solutions. We argue that these scaling solutions, if describing an accelerating expansion, are likely to be perturbatively unstable, for reasons identical to the perturbative instabilities in tree-level dS vacua.

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31

Bachlechner, Thomas C., David Marsh, Liam McAllister, and Timm Wrase. "Supersymmetric vacua in random supergravity." Journal of High Energy Physics 2013, no. 1 (2013). http://dx.doi.org/10.1007/jhep01(2013)136.

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32

Partipilo, Dario. "New methods for old problems: vacua of maximal D = 7 supergravities." Journal of High Energy Physics 2022, no. 9 (2022). http://dx.doi.org/10.1007/jhep09(2022)096.

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Abstract Finding vacua of supergravity theories is an outstanding problem which has been tackled in several ways, and with this work we add a new method to the puzzle. We analyse the scalar sector of maximal gauged supergravity theories in seven space-time dimensions. We look for vacua of the theory by varying the embedding tensor, instead of directly minimising the scalar potential. The set of quadratic constraints arising from this procedure has been solved by means of Evolution Strategies optimisation techniques, also adopted in Artificial Intelligence studies. We develop some methods to re

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33

Suh, Minwoo. "Brane-jet stabilities from Janus and Sasaki-Einstein." Journal of High Energy Physics 2023, no. 8 (2023). http://dx.doi.org/10.1007/jhep08(2023)164.

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Abstract We show that there are certain perturbatively stable non-supersymmetric AdS vacua which are also brane-jet stable. Also we extend the analysis of brane-jets to the AdS vacua from curved domain walls like Janus solutions. First, we apply the brane-jet analysis to the non-supersymmetric Janus solutions of type IIB supergravity found by Bak, Gutperle and Hirano. Second, we study the brane-jet of AdS4 vacua from eleven-dimensional supergravity on Sasaki-Einstein manifolds: the supersymmetric and the skew-whiffed Freund-Rubin, the Pope-Warner, and the Englert solutions. Third, we examine t

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34

Bansal, Sukruti, Silvia Nagy, Antonio Padilla, and Ivonne Zavala. "Unimodular vs nilpotent superfield approach to pure dS supergravity." Journal of High Energy Physics 2021, no. 1 (2021). http://dx.doi.org/10.1007/jhep01(2021)146.

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Abstract Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the general

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35

Dao, H. L., and Parinya Karndumri. "$$dS_5$$ vacua from matter-coupled 5D $$N=4$$ gauged supergravity." European Physical Journal C 79, no. 9 (2019). http://dx.doi.org/10.1140/epjc/s10052-019-7317-z.

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Abstract We study $$dS_5$$dS5 vacua within matter-coupled $$N=4$$N=4 gauged supergravity in five dimensions using the embedding tensor formalism. With a simple ansatz for solving the extremization and positivity of the scalar potential, we derive a set of conditions for the gauged supergravity to admit $$dS_5$$dS5 as maximally symmetric background solutions. The results provide a new approach for finding $$dS_5$$dS5 vacua in five-dimensional $$N=4$$N=4 gauged supergravity and explain a number of notable features pointed out in previous works. These conditions also determine the form of the gau

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36

Rigatos, Konstantinos S. "Non-integrability in AdS3 vacua." Journal of High Energy Physics 2021, no. 2 (2021). http://dx.doi.org/10.1007/jhep02(2021)032.

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Abstract We ask the question of classical integrability for certain (classes of) supergravity vacua that contain an AdS3 factor arising in massive IIA and IIB theories and realizing various and different amounts of supersymmetry. Our approach is based on a well-established method of analytic non-integrability for Hamiltonian systems. To detect a non-integrable sector we consider a non-trivially wrapped string soliton and study its fluctuations. We answer in the negative for each and every one of the supergravity solutions. That is, of course, modulo very specific limits where the metrics reduc

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37

Eloy, Camille. "Kaluza-Klein spectrometry for ${\rm AdS_{3}}$ vacua." SciPost Physics 10, no. 6 (2021). http://dx.doi.org/10.21468/scipostphys.10.6.131.

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We use exceptional field theory to compute Kaluza-Klein mass spectra around {AdS_{3}}AdS3 vacua that sit in half-maximal gauged supergravity in three dimensions. The formalism applies to any vacuum that arises from a consistent truncation of higher-dimensional supergravity, no matter what symmetries are preserved. We illustrate its efficiency by computing the spectra of {N}=(2,0)N=(2,0) and {N}=(1,1)N=(1,1) six-dimensional supergravities on {AdS_{3}}\times S^{3}AdS3×S3 and of type II supergravity on {AdS_{3}}\times S^{3}\times S^{3}\times S^{1}AdS3×S3×S3×S1.

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38

Berman, David, Thomas Fischbacher, Gianluca Inverso та Benjamin Scellier. "Vacua of ω-deformed SO(8) supergravity". Journal of High Energy Physics 2022, № 6 (2022). http://dx.doi.org/10.1007/jhep06(2022)133.

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Abstract We perform a detailed analysis of the vacua of ω-deformed SO(8) supergravity in four dimensions. In particular, using Tensorflow-based numerical methods, we track how the equilibria of the theory change when varying the electric-magnetic deformation parameter ω. Apart from describing various properties of different equilibria (390 in total), we show that as ω is deformed, the SO(3), $$ \mathcal{N} $$ N = 1 vacuum of the de Wit-Nicolai theory becomes equivalent to a critical point in U(4) ⋉ ℝ12 gauged supergravity with a known uplift in IIB supergravity. The procedure employed here to

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39

Dall’Agata, G., G. Inverso, and D. Partipilo. "Old and new vacua of 5D maximal supergravity." Journal of High Energy Physics 2021, no. 4 (2021). http://dx.doi.org/10.1007/jhep04(2021)039.

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Abstract We look for critical points with U(2) residual symmetry in 5-dimensional maximally supersymmetric gauged supergravity, by varying the embedding tensor, rather than directly minimizing the scalar potential. We recover all previously known vacua and we find four new vacua, with different gauge groups and cosmological constants. We provide the first example of a maximal supergravity model in D ≥ 4 having critical points with both positive and vanishing cosmological constant. For each vacuum we also compute the full mass spectrum. All results are analytic.

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40

Malek, Emanuel, Hermann Nicolai, and Henning Samtleben. "Tachyonic Kaluza-Klein modes and the AdS swampland conjecture." Journal of High Energy Physics 2020, no. 8 (2020). http://dx.doi.org/10.1007/jhep08(2020)159.

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Abstract We compute the Kaluza-Klein spectrum of the non-supersymmetric SO(3) × SO(3)-invariant AdS4 vacuum of 11-dimensional supergravity, whose lowest-lying Kaluza-Klein modes belong to a consistent truncation to 4-dimensional $$ \mathcal{N} $$ N = 8 supergravity and are stable. We show that, nonetheless, the higher Kaluza-Klein modes become tachyonic so that this non-supersymmetric AdS4 vacuum is perturbatively unstable within 11-dimensional supergravity. This represents the first example of unstable higher Kaluza-Klein modes and provides further evidence for the AdS swampland conjecture, w

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41

Karndumri, Parinya, and Chawakorn Maneerat. "Supersymmetric Janus solutions in $$\omega $$-deformed $$N=8$$ gauged supergravity." European Physical Journal C 81, no. 9 (2021). http://dx.doi.org/10.1140/epjc/s10052-021-09582-y.

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AbstractWe give a large class of supersymmetric Janus solutions in $$\omega $$ ω -deformed (dyonic) SO(8) maximal gauged supergravity with $$\omega =\frac{\pi }{8}$$ ω = π 8 . Unlike the purely electric counterpart, the dyonic SO(8) gauged supergravity exhibits a richer structure of $$AdS_4$$ A d S 4 vacua with $$N=8,2,1,1$$ N = 8 , 2 , 1 , 1 supersymmetries and SO(8), U(3), $$G_2$$ G 2 and SU(3) symmetries, respectively. Similarly, domain walls interpolating among these critical points show a very rich structure as well. In this paper, we show that this gauged supergravity also accommodates a

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42

Eloy, Camille, Michele Galli, and Emanuel Malek. "Adding fluxes to consistent truncations: IIB supergravity on AdS3 × S3 × S3 × S1." Journal of High Energy Physics 2023, no. 11 (2023). http://dx.doi.org/10.1007/jhep11(2023)049.

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Abstract We use E8(8) Exceptional Field Theory to construct the consistent truncation of IIB supergravity on S3× S3× S1 to maximal 3-dimensional $$ \mathcal{N} $$ N = 16 gauged supergravity containing the $$ \mathcal{N} $$ N = (4, 4) AdS3 vacuum. We explain how to achieve this by adding a 7-form flux to the S1 reduction of the dyonic E7(7) truncation on S3× S3 previously constructed in the literature. Our truncation Ansatz includes, in addition to the $$ \mathcal{N} $$ N = (4, 4) vacuum, a host of moduli breaking some or all of the supersymmetries. We explicitly construct the uplift of a subse

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43

Louis, Jan, Paul Smyth, and Hagen Triendl. "Supersymmetric vacua in N = 2 supergravity." Journal of High Energy Physics 2012, no. 8 (2012). http://dx.doi.org/10.1007/jhep08(2012)039.

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44

Faedo, Federico, Nicolò Petri, and Alessia Segati. "Defects in 4d SCFTs from supergravity and holographic renormalization." Journal of High Energy Physics 2025, no. 5 (2025). https://doi.org/10.1007/jhep05(2025)070.

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Abstract Type IIB string theory admits Janus solutions connecting AdS5 vacua. These geometries correspond to interface conformal field theories and are naturally described in five-dimensional supergravity as AdS4 foliations over an interval. In this work, we introduce a novel type of Janus solution in AdS5, featuring AdS2 × S 2 foliations instead of AdS4. We interpret these solutions as the supergravity duals of line defects in four-dimensional SCFTs and we discuss their D-brane engineering. Our primary tool is Romans supergravity in five dimensions, which provides a simple Type IIB truncation

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45

Suh, Minwoo. "The non-SUSY AdS6 and AdS7 fixed points are brane-jet unstable." Journal of High Energy Physics 2020, no. 10 (2020). http://dx.doi.org/10.1007/jhep10(2020)010.

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Abstract In six- and seven-dimensional gauged supergravity, each scalar potential has one supersymmetric and one non-supersymmetric fixed points. The non-supersymmetric AdS7 fixed point is perturbatively unstable. On the other hand, the non-supersymmetric AdS6 fixed point is known to be perturbatively stable. In this note we examine the newly proposed non-perturbative decay channel, called brane-jet instabilities of the AdS6 and AdS7 vacua. We find that when they are uplifted to massive type IIA and eleven- dimensional supergravity, respectively, the non-supersymmetric AdS6 and AdS7 vacua are

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46

Bobev, Nikolay, Thomas Fischbacher, Fridrik Freyr Gautason, and Krzysztof Pilch. "New AdS4 vacua in dyonic ISO(7) gauged supergravity." Journal of High Energy Physics 2021, no. 2 (2021). http://dx.doi.org/10.1007/jhep02(2021)215.

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Abstract We identify 219 AdS4 solutions in four-dimensional dyonically gauged ISO(7) $$ \mathcal{N} $$ N = 8 supergravity and present some of their properties. One of the new solutions preserves $$ \mathcal{N} $$ N = 1 supersymmetry and provides a rare explicit example of an AdS4 vacuum dual to a 3d SCFT with no continuous global symmetry. There are also two new non-supersymmetric solutions for which all 70 scalar fields in the supergravity theory have masses above the BF bound. All of these AdS4 solutions can be uplifted to massive type IIA supergravity. Motivated by this we present the low l

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47

Jockers, Hans, and Sören Kotlewski. "Geometry of N=2 Minkowski vacua of gauged N=2 supergravity theories in four dimensions." Physical Review D 110, no. 4 (2024). http://dx.doi.org/10.1103/physrevd.110.046019.

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Gauging isometries of four-dimensional N=2 supergravity theories yields an N=2 supersymmetric theory with a scalar potential. In this paper, we study the well-known constraints for four-dimensional N=2 Minkowski vacua of such theories. We propose that classically a projective special Kähler submanifold of the projective Kähler target space of the ungauged theory describes the moduli space of the complex scalar fields of massless vector multiplets for N=2 Minkowski vacua configurations, which then receives quantum corrections from integrating out massive fields. Subloci of projective special Kä

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48

Cribiori, Niccolò, and Carmine Montella. "Quantum gravity constraints on scale separation and de Sitter in five dimensions." Journal of High Energy Physics 2023, no. 5 (2023). http://dx.doi.org/10.1007/jhep05(2023)178.

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Abstract We give evidence that supersymmetric anti-de Sitter vacua of five-dimensional supergravity cannot be scale separated as a consequence of quantum gravity constraints, such as the weak gravity conjecture or the species scale. We show this in a model-independent way for the minimal and the maximal theory and we believe that the argument can be extended to any amount of preserved supercharges in the between. If combined with previous works stating that non-supersymmetric anti-de Sitter vacua must be unstable, our results suggest that five-dimensional effective field theories in anti-de Si

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49

Cribiori, Niccolò, and Gianguido Dall’Agata. "Weak gravity versus scale separation." Journal of High Energy Physics 2022, no. 6 (2022). http://dx.doi.org/10.1007/jhep06(2022)006.

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Abstract We give evidence that fully supersymmetric Anti-de Sitter vacua of extended supergravity with a residual gauge group containing an abelian factor cannot be scale separated as a consequence of the weak gravity conjecture. We prove this for N = 2 and N = 8 supergravity and we explain how our argument applies also to vacua with partially broken, but extended residual supersymmetry. We finally discuss possible loopholes and especially how certain N = 1 models can evade our reasoning. Our results suggest that N = 0, 1 supersymmetry at the lagrangian level might be the most promising chance

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50

Dao, H. L., and Parinya Karndumri. "$$dS_4$$ vacua from matter-coupled 4D $$N=4$$ gauged supergravity." European Physical Journal C 79, no. 9 (2019). http://dx.doi.org/10.1140/epjc/s10052-019-7318-y.

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Abstract We study $$dS_4$$dS4 vacua within matter-coupled $$N=4$$N=4 gauged supergravity in the embedding tensor formalism. We derive a set of conditions for the existence of $$dS_4$$dS4 solutions by using a simple ansatz for solving the extremization and positivity of the scalar potential. We find two classes of gauge groups that lead to $$dS_4$$dS4 vacua. One of them consists of gauge groups of the form $$G_{\text {e}}\times G_{\text {m}}\times H$$Ge×Gm×H with H being a compact group and $$G_{\text {e}}\times G_{\text {m}}$$Ge×Gm a non-compact group with $$SO(3)\times SO(3)$$SO(3)×SO(3) subg

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