Abstract
We find the superpotential governing the supersymmetric warped M-theory solution with a transverse Stenzel space found by Cvetič, Gibbons, Lü and Pope in hep-th/0012011, and use this superpotential to extract and solve the twelve coupled equations underlying the first-order backreacted solution of a stack of anti-M2 branes in this space. These anti-M2 branes were analyzed recently in a probe approximation by Klebanov and Pufu, who conjectured that they should be dual to a metastable vacuum of a supersymmetric 2 + 1 dimensional theory. We find that the would-be supergravity dual to such a metastable vacuum must have an infrared singularity and discuss whether this singularity is acceptable or not. Given that a similar singularity appears when placing anti-D3 branes in the Klebanov-Strassler solution, our work strengthens the possibility that anti-branes in warped throats do not give rise to metastable vacua.
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K.A. Intriligator, N. Seiberg and D. Shih, Dynamical SUSY breaking in meta-stable vacua, JHEP 04 (2006) 021 [hep-th/0602239] [SPIRES].
Y. Shadmi and Y. Shirman, Dynamical supersymmetry breaking, Rev. Mod. Phys. 72 (2000) 25 [hep-th/9907225] [SPIRES].
A.E. Nelson and N. Seiberg, R symmetry breaking versus supersymmetry breaking, Nucl. Phys. B 416 (1994) 46 [hep-ph/9309299] [SPIRES].
K.A. Intriligator, N. Seiberg and D. Shih, Supersymmetry breaking, R-symmetry breaking and metastable vacua, JHEP 07 (2007) 017 [hep-th/0703281] [SPIRES].
K.A. Intriligator and N. Seiberg, Lectures on supersymmetry breaking, Class. Quant. Grav. 24 (2007) S741 [hep-ph/0702069] [SPIRES].
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] [SPIRES].
H. Ooguri and Y. Ookouchi, Meta-stable supersymmetry breaking vacua on intersecting branes, Phys. Lett. B 641 (2006) 323 [hep-th/0607183] [SPIRES].
S. Franco, I. Garcia-Etxebarria and A.M. Uranga, Non-supersymmetric meta-stable vacua from brane configurations, JHEP 01 (2007) 085 [hep-th/0607218] [SPIRES].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [SPIRES].
K. Hori, H. Ooguri and Y. Oz, Strong coupling dynamics of four-dimensional N = 1 gauge theories from M-theory fivebrane, Adv. Theor. Math. Phys. 1 (1998) 1 [hep-th/9706082] [SPIRES].
A. Brandhuber, N. Itzhaki, V. Kaplunovsky, J. Sonnenschein and S. Yankielowicz, Comments on the M-theory approach to N = 1 SQCD and brane dynamics, Phys. Lett. B 410 (1997) 27 [hep-th/9706127] [SPIRES].
A. Giveon and D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys. 71 (1999) 983 [hep-th/9802067] [SPIRES].
S. Kachru, J. Pearson and H.L. Verlinde, Brane/flux annihilation and the string dual of a non-supersymmetric field theory, JHEP 06 (2002) 021 [hep-th/0112197] [SPIRES].
O. DeWolfe, S. Kachru and H.L. Verlinde, The giant inflaton, JHEP 05 (2004) 017 [hep-th/0403123] [SPIRES].
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] [SPIRES].
R.C. Myers, Dielectric-branes, JHEP 12 (1999) 022 [hep-th/9910053] [SPIRES].
J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [SPIRES].
I.R. Klebanov and S.S. Pufu, M-branes and metastable states, arXiv:1006.3587 [SPIRES].
M. Stenzel, Ricci-flat metrics on the complexification of a compact rank one symmetric space, Manuscripta Math. 80 (1993) 1.
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] [SPIRES].
I. Bena, The M-theory dual of a 3 dimensional theory with reduced supersymmetry, Phys. Rev. D 62 (2000) 126006 [hep-th/0004142] [SPIRES].
I. Bena, M. Graña and N. Halmagyi, On the existence of meta-stable vacua in Klebanov-Strassler, JHEP 09 (2010) 087 [arXiv:0912.3519] [SPIRES].
S. Kachru et al., Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [SPIRES].
O. DeWolfe, S. Kachru and M. Mulligan, A gravity dual of metastable dynamical supersymmetry breaking, Phys. Rev. D 77 (2008) 065011 [arXiv:0801.1520] [SPIRES].
I.R. Klebanov and A.A. Tseytlin, Gravity duals of supersymmetric SU(N) × SU(N + M) gauge theories, Nucl. Phys. B 578 (2000) 123 [hep-th/0002159] [SPIRES].
P. McGuirk, G. Shiu and Y. Sumitomo, Non-supersymmetric infrared perturbations to the warped deformed conifold, Nucl. Phys. B 842 (2010) 383 [arXiv:0910.4581] [SPIRES].
G.T. Horowitz and R.C. Myers, The value of singularities, Gen. Rel. Grav. 27 (1995) 915 [gr-qc/9503062] [SPIRES].
V. Borokhov and S.S. Gubser, Non-supersymmetric deformations of the dual of a confining gauge theory, JHEP 05 (2003) 034 [hep-th/0206098] [SPIRES].
G. Papadopoulos and A.A. Tseytlin, Complex geometry of conifolds and 5-brane wrapped on 2-sphere, Class. Quant. Grav. 18 (2001) 1333 [hep-th/0012034] [SPIRES].
D. Cassani and A.F. Faedo, A supersymmetric consistent truncation for conifold solutions, Nucl. Phys. B 843 (2011) 455 [arXiv:1008.0883] [SPIRES].
I. Bena, G. Giecold, M. Graña, N. Halmagyi and F. Orsi, Supersymmetric consistent truncations of IIB on T(1, 1), JHEP 04 (2011) 021 [arXiv:1008.0983] [SPIRES].
J.M. Maldacena and H.S. Nastase, The supergravity dual of a theory with dynamical supersymmetry breaking, JHEP 09 (2001) 024 [hep-th/0105049] [SPIRES].
P. McFadden and K. Skenderis, The holographic universe, J. Phys. Conf. Ser. 222 (2010) 012007 [arXiv:1001.2007] [SPIRES].
C. Krishnan and S. Kuperstein, The mesonic branch of the deformed conifold, JHEP 05 (2008) 072 [arXiv:0802.3674] [SPIRES].
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] [SPIRES].
J. Blaback et al., Smeared versus localised sources in flux compactifications, JHEP 12 (2010) 043 [arXiv:1009.1877] [SPIRES].
A. Giveon, D. Kutasov and O. Lunin, Spontaneous SUSY breaking in various dimensions, Nucl. Phys. B 822 (2009) 127 [arXiv:0904.2175] [SPIRES].
G. Giecold, unpublished.
M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, Supersymmetric non-singular fractional D2-branes and NS-NS 2-branes, Nucl. Phys. B 606 (2001) 18 [hep-th/0101096] [SPIRES].
G.C. Giecold, Finite-temperature fractional D2-branes and the deconfinement transition in 2 + 1 dimensions, JHEP 03 (2010) 109 [arXiv:0912.1558] [SPIRES].
S. Kuperstein and J. Sonnenschein, Analytic non-supersymmetric background dual of a confining gauge theory and the corresponding plane wave theory of hadrons, JHEP 02 (2004) 015 [hep-th/0309011] [SPIRES].
A. Ceresole, G. Dall’Agata, R. D’Auria and S. Ferrara, M-theory on the Stiefel manifold and 3D conformal field theories, JHEP 03 (2000) 011 [hep-th/9912107] [SPIRES].
P. Candelas and X.C. de la Ossa, Comments on conifolds, Nucl. Phys. B 342 (1990) 246 [SPIRES].
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] [SPIRES].
D.L. Jafferis, Quantum corrections to N = 2 Chern-Simons theories with flavor and their AdS 4 duals, arXiv:0911.4324 [SPIRES].
I. Bena, G. Giecold, M. Graña and N. Halmagyi, On the inflaton potential from antibranes in warped throats, arXiv:1011.2626 [SPIRES].
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [SPIRES].
V. Balasubramanian, P. Kraus, A.E. Lawrence and S.P. Trivedi, Holographic probes of Anti-de Sitter space-times, Phys. Rev. D 59 (1999) 104021 [hep-th/9808017] [SPIRES].
A. Bergman and C.P. Herzog, The volume of some non-spherical horizons and the AdS/CFT correspondence, JHEP 01 (2002) 030 [hep-th/0108020] [SPIRES].
M. Graña and J. Polchinski, Supersymmetric three-form flux perturbations on AdS 5, Phys. Rev. D 63 (2001) 026001 [hep-th/0009211] [SPIRES].
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Bena, I., Giecold, G. & Halmagyi, N. The backreaction of anti-M2 branes on a warped Stenzel space. J. High Energ. Phys. 2011, 120 (2011). https://doi.org/10.1007/JHEP04(2011)120
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DOI: https://doi.org/10.1007/JHEP04(2011)120