Abstract
We study AdS7 vacua of massive type IIA string theory compactified on a 3-sphere with H 3 flux and anti-D6-branes. In such backgrounds, the anti-brane backreaction is known to generate a singularity in the H 3 energy density, whose interpretation has not been understood so far. We first consider supersymmetric solutions of this setup and give an analytic proof that the flux singularity is resolved there by a polarization of the anti-D6-branes into a D8-brane, which wraps a finite 2-sphere inside of the compact space. To this end, we compute the potential for a spherical probe D8-brane on top of a background with backreacting anti-D6-branes and show that it has a local maximum at zero radius and a local minimum at a finite radius of the 2-sphere. The polarization is triggered by a term in the potential due to the AdS curvature and does therefore not occur in non-compact setups where the 7d external spacetime is Minkowski. We furthermore find numerical evidence for the existence of non-supersymmetric solutions in our setup. This is supported by the observation that the general solution to the equations of motion has a continuous parameter that is suggestive of a modulus and appears to control supersymmetry breaking. Analyzing the polarization potential for the non-supersymmetric solutions, we find that the flux singularities are resolved there by brane polarization as well.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [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].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χSB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [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].
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, On metastable vacua and the warped deformed conifold: analytic results, Class. Quant. Grav. 30 (2013) 015003 [arXiv:1102.2403] [INSPIRE].
I. Bena, G. Giecold, M. Graña, N. Halmagyi and S. Massai, The backreaction of anti-D3 branes on the Klebanov-Strassler geometry, JHEP 06 (2013) 060 [arXiv:1106.6165] [INSPIRE].
O. DeWolfe, S. Kachru and M. Mulligan, A gravity dual of metastable dynamical supersymmetry breaking, Phys. Rev. D 77 (2008) 065011 [arXiv:0801.1520] [INSPIRE].
A. Dymarsky, On gravity dual of a metastable vacuum in Klebanov-Strassler theory, JHEP 05 (2011) 053 [arXiv:1102.1734] [INSPIRE].
S. Massai, A comment on anti-brane singularities in warped throats, arXiv:1202.3789 [INSPIRE].
J. Blabäck et al., The problematic backreaction of SUSY-breaking branes, JHEP 08 (2011) 105 [arXiv:1105.4879] [INSPIRE].
J. Blabäck et al., (Anti-)brane backreaction beyond perturbation theory, JHEP 02 (2012) 025 [arXiv:1111.2605] [INSPIRE].
I. Bena, M. Graña, S. Kuperstein and S. Massai, Anti-D3 branes: singular to the bitter end, Phys. Rev. D 87 (2013) 106010 [arXiv:1206.6369] [INSPIRE].
I. Bena, G. Giecold and N. Halmagyi, The backreaction of anti-M 2 branes on a warped Stenzel space, JHEP 04 (2011) 120 [arXiv:1011.2195] [INSPIRE].
G. Giecold, E. Goi and F. Orsi, Assessing a candidate IIA dual to metastable supersymmetry-breaking, JHEP 02 (2012) 019 [arXiv:1108.1789] [INSPIRE].
S. Massai, Metastable vacua and the backreacted Stenzel geometry, JHEP 06 (2012) 059 [arXiv:1110.2513] [INSPIRE].
G. Giecold, F. Orsi and A. Puhm, Insane anti-membranes?, JHEP 03 (2014) 041 [arXiv:1303.1809] [INSPIRE].
W. Cottrell, J. Gaillard and A. Hashimoto, Gravity dual of dynamically broken supersymmetry, JHEP 08 (2013) 105 [arXiv:1303.2634] [INSPIRE].
J. Blabäck, A note on M2-branes in opposite charge, Phys. Rev. D 89 (2014) 065004 [arXiv:1309.2640] [INSPIRE].
I. Bena, M. Graña, S. Kuperstein and S. Massai, Tachyonic anti-M 2 branes, JHEP 06 (2014) 173 [arXiv:1402.2294] [INSPIRE].
F.F. Gautason, D. Junghans and M. Zagermann, Cosmological constant, near brane behavior and singularities, JHEP 09 (2013) 123 [arXiv:1301.5647] [INSPIRE].
Y. Aghababaie et al., Warped brane worlds in six-dimensional supergravity, JHEP 09 (2003) 037 [hep-th/0308064] [INSPIRE].
C.P. Burgess, A. Maharana, L. van Nierop, A.A. Nizami and F. Quevedo, On brane back-reaction and de Sitter solutions in higher-dimensional supergravity, JHEP 04 (2012) 018 [arXiv:1109.0532] [INSPIRE].
D. Junghans, Dynamics of warped flux compactifications with backreacting anti-branes, arXiv:1402.4571 [INSPIRE].
J. Blabäck, U.H. Danielsson and T. Van Riet, Resolving anti-brane singularities through time-dependence, JHEP 02 (2013) 061 [arXiv:1202.1132] [INSPIRE].
I. Bena, A. Buchel and O.J.C. Dias, Horizons cannot save the landscape, Phys. Rev. D 87 (2013) 063012 [arXiv:1212.5162] [INSPIRE].
I. Bena, J. Blabäck, U.H. Danielsson and T. Van Riet, Antibranes cannot become black, Phys. Rev. D 87 (2013) 104023 [arXiv:1301.7071] [INSPIRE].
A. Buchel and D.A. Galante, Cascading gauge theory on dS 4 and string theory landscape, Nucl. Phys. B 883 (2014) 107 [arXiv:1310.1372] [INSPIRE].
S.S. Gubser, Curvature singularities: the good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [INSPIRE].
I. Bena, M. Graña, S. Kuperstein and S. Massai, Polchinski-Strassler does not uplift Klebanov-Strassler, JHEP 09 (2013) 142 [arXiv:1212.4828] [INSPIRE].
I. Bena et al., Persistent anti-brane singularities, JHEP 10 (2012) 078 [arXiv:1205.1798] [INSPIRE].
M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, Ricci flat metrics, harmonic forms and brane resolutions, Commun. Math. Phys. 232 (2003) 457 [hep-th/0012011] [INSPIRE].
F. Apruzzi, M. Fazzi, D. Rosa and A. Tomasiello, All AdS 7 solutions of type-II supergravity, JHEP 04 (2014) 064 [arXiv:1309.2949] [INSPIRE].
U.H. Danielsson, G. Dibitetto, M. Fazzi and T. Van Riet, A note on smeared branes in flux vacua and gauged supergravity, JHEP 04 (2014) 025 [arXiv:1311.6470] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive energy in anti-de Sitter backgrounds and gauged extended supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
D. Schmidt, Numerical computation of localized D-brane solutions, Master’s thesis, Leibniz Universität, Hannover Germany (2013).
J. Blabäck et al., Smeared versus localised sources in flux compactifications, JHEP 12 (2010) 043 [arXiv:1009.1877] [INSPIRE].
E. Witten, Dimensional reduction of superstring models, Phys. Lett. B 155 (1985) 151 [INSPIRE].
C.P. Burgess, A. Font and F. Quevedo, Low-energy effective action for the superstring, Nucl. Phys. B 272 (1986) 661 [INSPIRE].
D. Gaiotto and A. Tomasiello, Holography for (1, 0) theories in six dimensions, arXiv:1404.0711 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1402.6040
New address since March 1, 2014: Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität, Jena, Fröbelstieg 1, 07743 Jena, Germany. (Daniel Schmidt)
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Junghans, D., Schmidt, D. & Zagermann, M. Curvature-induced resolution of anti-brane singularities. J. High Energ. Phys. 2014, 34 (2014). https://doi.org/10.1007/JHEP10(2014)034
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2014)034