Moduli stabilization, large-volume dS minimum without image-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi–Yauʹs Original Research Article

We consider two sets of issues in this paper. The first has to do with moduli stabilization, existence of “area codes” [A. Giryavets, New attractors and area codes, JHEP 0603 (2006) 020, ] and the possibility of getting a non-supersymmetric dS minimum without the addition of image-branes as in KKLT for type II flux compactifications. The second has to do with the “inverse problem” [K. Saraikin, C. Vafa, Non-supersymmetric black holes and topological strings, ] and “fake superpotentials” [A. Ceresole, G. DallʹAgata, Flow equations for non-BPS extremal black holes, JHEP 0703 (2007) 110, ] for extremal (non-)supersymmetric black holes in type II compactifications. We use (orientifold of) a “Swiss cheese” Calabi–Yau [J.P. Conlon, F. Quevedo, K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 0508 (2005) 007, ] expressed as a degree-18 hypersurface in image in the “large-volume-scenario” limit [V. Balasubramanian, P. Berglund, J.P. Conlon, F. Quevedo, Systematics of moduli stabilisation in Calabi–Yau flux compactifications, JHEP 0503 (2005) 007, ]. The main result of our paper is that we show that by including non-perturbative image and instanton corrections in the Kähler potential and superpotential [T.W. Grimm, Non-perturbative corrections and modularity in image type IIB compactifications, ], it may be possible to obtain a large-volume non-supersymmetric dS minimum without the addition of anti-D3 branes a la KKLT. The chosen Calabi–Yau has been of relevance also from the point of other studies of Kähler moduli stabilization via non-perturbative instanton contributions [F. Denef, M.R. Douglas, B. Florea, Building a better racetrack, JHEP 0406 (2004) 034, ] and non-supersymmetric AdS vacua (and their subsequent dS-uplifts) using image corrections to the Kähler potential [V. Balasubramanian, P. Berglund, J.P. Conlon, F. Quevedo, Systematics of moduli stabilisation in Calabi–Yau flux compactifications, JHEP 0503 (2005) 007, ; K. Becker, M. Becker, M. Haack, J. Louis, Supersymmetry breaking and alphaʹ-corrections to flux induced potentials, JHEP 0206 (2002) 060, ; A. Westphal, de Sitter string vacua from Kähler uplifting, JHEP 0703 (2007) 102, ; V. Balasubramanian, P. Berglund, Stringy corrections to Kähler potentials, SUSY breaking, and the cosmological constant problem, JHEP 0411 (2004) 085, ].