Abstract
We construct an M-theory background dual to the metastable state recently discussed by Klebanov and Pufu, which corresponds to placing a stack of anti-M2 branes at the tip of a warped Stenzel space. With this purpose we analytically solve for the linearized non-supersymmetric deformations around the warped Stenzel space, preserving the SO(5) symmetries of the supersymmetric background, and which interpolate between the IR and UV region. We identify the supergravity solution which corresponds to a stack of \( \overline N \) backreacting anti-M2 branes by fixing all the 12 integration constants in terms of \( \overline N \). While in the UV this solution has the desired features to describe the conjectured metastable state of the dual (2 + 1)–dimensional theory, in the IR it suffers from a singularity in the four-form flux, which we describe in some details.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K.A. Intriligator, N. Seiberg and D. Shih, Dynamical SUSY breaking in meta-stable vacua, JHEP 04 (2006) 021 [hep-th/0602239] [INSPIRE].
I. Bena, E. Gorbatov, S. Hellerman, N. Seiberg and D. Shih, A note on (meta)stable brane configurations in MQCD, JHEP 11 (2006) 088 [hep-th/0608157] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χ SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
S. Kachru, J. Pearson and H.L. Verlinde, Brane/flux annihilation and the string dual of a nonsupersymmetric field theory, JHEP 06 (2002) 021 [hep-th/0112197] [INSPIRE].
O. DeWolfe, S. Kachru and H.L. Verlinde, The giant inflaton, JHEP 05 (2004) 017 [hep-th/0403123] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
I. Bena, M. Graña and N. Halmagyi, On the existence of meta-stable vacua in Klebanov-Strassler, JHEP 09 (2010) 087 [arXiv:0912.3519] [INSPIRE].
I. Bena, G. Giecold, M. Graña, N. Halmagyi and S. Massai, The backreaction of anti-D3 branes on the Klebanov-Strassler geometry, arXiv:1106.6165 [INSPIRE].
A. Dymarsky, On gravity dual of a metastable vacuum in Klebanov-Strassler theory, JHEP 05 (2011) 053 [arXiv:1102.1734] [INSPIRE].
I.R. Klebanov and S.S. Pufu, M-branes and metastable states, JHEP 08 (2011) 035 [arXiv:1006.3587] [INSPIRE].
M. Stenzel, Ricci-at metrics on the complexification of a compact rank one symmetric space, Manuscripta Math. 80 (1993) 1.
M. Cvetič, G. Gibbons, H. Lü and C. Pope, Ricci at metrics, harmonic forms and brane resolutions, Commun. Math. Phys. 232 (2003) 457 [hep-th/0012011] [INSPIRE].
I. Bena, G. Giecold and N. Halmagyi, The backreaction of anti-M2 branes on a warped Stenzel space, JHEP 04 (2011) 120 [arXiv:1011.2195] [INSPIRE].
V. Borokhov and S.S. Gubser, Nonsupersymmetric deformations of the dual of a confining gauge theory, JHEP 05 (2003) 034 [hep-th/0206098] [INSPIRE].
G. Giecold and N. Halmagyi, unpublished.
G. Giecold, E. Goi and F. Orsi, Assessing a candidate IIA dual to metastable supersymmetry-breaking, JHEP 02 (2012) 019 [arXiv:1108.1789] [INSPIRE].
D. Martelli and J. Sparks, AdS(4)/CFT(3) duals from M2-branes at hypersurface singularities and their deformations, JHEP 12 (2009) 017 [arXiv:0909.2036] [INSPIRE].
I. Bena, G. Giecold, M. Graña and N. Halmagyi, On the inflaton potential from antibranes in warped throats, arXiv:1011.2626 [INSPIRE].
I. Bena, G. Giecold, M. Graña, N. Halmagyi and S. Massai, On metastable vacua and the warped deformed conifold: analytic results, arXiv:1102.2403 [INSPIRE].
S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. B 608 (2001) 477-478] [hep-th/9906070] [INSPIRE].
O. Aharony, A. Hashimoto, S. Hirano and P. Ouyang, D-brane charges in gravitational duals of 2 + 1 dimensional gauge theories and duality cascades, JHEP 01 (2010) 072 [arXiv:0906.2390] [INSPIRE].
A. Hashimoto and P. Ouyang, Quantization of charges and fluxes in warped Stenzel geometry, JHEP 06 (2011) 124 [arXiv:1104.3517] [INSPIRE].
A. Bergman and C.P. Herzog, The volume of some nonspherical horizons and the AdS/CFT correspondence, JHEP 01 (2002) 030 [hep-th/0108020] [INSPIRE].
A. Hashimoto, Comments on domain walls in holographic duals of mass deformed conformal field theories, JHEP 07 (2011) 031 [arXiv:1105.3687] [INSPIRE].
P. McGuirk, G. Shiu and Y. Sumitomo, Non-supersymmetric infrared perturbations to the warped deformed conifold, Nucl. Phys. B 842 (2011) 383 [arXiv:0910.4581] [INSPIRE].
J. Blaback et al., Smeared versus localised sources in flux compactifications, JHEP 12 (2010) 043 [arXiv:1009.1877] [INSPIRE].
J. Blaback et al., The problematic backreaction of SUSY-breaking branes, JHEP 08 (2011) 105 [arXiv:1105.4879] [INSPIRE].
S. Kachru et al., Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [INSPIRE].
S.S. Pufu, I.R. Klebanov, T. Klose and J. Lin, Green’s functions and non-singlet glueballs on deformed conifolds, J. Phys. A 44 (2011) 055404 [arXiv:1009.2763] [INSPIRE].
M. Graña and J. Polchinski, Supersymmetric three form flux perturbations on AdS 5, Phys. Rev. D 63 (2001) 026001 [hep-th/0009211] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1110.2513
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Massai, S. Metastable vacua and the backreacted Stenzel geometry. J. High Energ. Phys. 2012, 59 (2012). https://doi.org/10.1007/JHEP06(2012)059
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2012)059