Abstract
We study warped compactifications of string/M theory with the help of effective potentials, continuing previous work of the last two authors and Michael R. Douglas presented in (On the boundedness of effective potentials arising from string compactifications. Communications in Mathematical Physics 325(3):847–878, 2014). Under physically reasonable assumptions, we provide a mathematically rigorous proof of the existence of positive local minima of a large class of effective potentials. The dynamics of the conformal factor of the internal metric, which is responsible for instabilities in these constructions, is explored, and such instabilities are investigated in the context of de Sitter vacua. We prove existence results for the equations of motion in the case of a slowly varying warp factor, and the stability of such solutions is also addressed. These solutions are a family of meta-stable de Sitter vacua from type IIB string theory in a general non-supersymmetric setup.
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Andriot, D., Goi, E., Minasian, R., Petrini, M.: Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory. JHEP 1105, 028 (2011). arXiv:1003.3774v2 [hep-th]
Candelas P., Horowitz G., Strominger A., Witten E.: Vacuum configurations for superstrings. Nucl. Phys. B 258, 46–74 (1985)
Dabholkar, S.P., Disconzi, M.M., Pingali, V.P.: in preparation.
DeWolfe, O., Giryavets, A., Kachru, S., Taylor, W.: Type IIA moduli stabilization. JHEP 0507, 066 (2005). arXiv:hep-th/0505160v3
Disconzi, M.M.: A note on quantization in the presence of gravitational shock waves. Mod. Phys. Lett. A. 28(31), 1350111 (2013). arXiv:1304.4917 [gr-qc]
Disconzi, M.M., Douglas, M.R., Pingali, V.P.: On the boundedness of effective potentials arising from string compactifications. Commun. Math. Phys. 325(3), 847–878 (2014). arXiv:1206.1885 [math-ph]
Disconzi, M.M., Khuri, M.A.: Compactness and non-compactness for Yamabe problem on manifolds with boundary. J. Reine Angew. Math. (Crelle’s J), to appear. arXiv:1201.4559 [math.DG]
Douglas, M.R.: Effective potential and warp dynamics. JHEP 1003, 071 (2010). arXiv:0911.3378v4 [hep-th]
Douglas, M., Kachru, S.: Flux compactification. Rev. Mod. Phys. 79, 733–796 (2007). arXiv:0610102v3 [hep-th]
Giddings, S.: The fate of four-dimensions. Phys. Rev. D 68, 026006 (2003). arXiv:0303031v2 [hep-th]
Giddings, S.B., Kachru, S., Polchinski, J.: Hierarchies from fluxes in string compactifications. Phys. Rev. D66, 106006 (2002). arXiv:hep-th/0105097
Grana, M.: Flux compactifications in string theory: a comprehensive review. Phys. Rep. 423, 91–158. arXiv:0509003v3 [hep-th]
Kachru, S., Kallosh, R., Linde, A.D., Trivedi, S.P.: De Sitter vacua in string theory. Phys. Rev. D 68, 046005 (2003). [hep-th/0301240]
Kachru, S., Schulz, M., Trivedi, S.: Moduli stabilization from fluxes in a simple IIB orientifold. JHEP 0310, 007 (2003). arXiv:hep-th/0201028
Maldacena, J., Nunez, C.: Supergravity description of field theories on curved manifolds and a no go theorem. Int. J. Mod. Phys. A16, 822–855 (2001). arXiv:0007018v2 [hep-th]
Schoen, R., Yau, S.-T.: Lectures on differential geometry. In: Conference Proceedings and Lecture Notes in Geometry and Topology, vol I. International Press, USA (1994)
Silverstein, E.: Simple de Sitter solutions. Phys. Rev. D77, 106006 (2008). arXiv:0712.1196v4 [hep-th]
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We would like to thank Michael R. Douglas for fruitful discussions on this topic at various stages. Marcelo M. Disconzi is supported by NSF Grant PHY-1305705.
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Dabholkar, S.P., Disconzi, M.M. & Pingali, V.P. Remarks on Positive Energy Vacua via Effective Potentials in String Theory. Lett Math Phys 104, 893–910 (2014). https://doi.org/10.1007/s11005-014-0694-1
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DOI: https://doi.org/10.1007/s11005-014-0694-1