Abstract
We study a supersymmetry breaking deformation of the M-theory background found in arXiv:hep-th/0012011. The supersymmetric solution is a warped product of \( {\mathbb{R}^{2,1}} \) and the 8-dimensional Stenzel space, which is a higher dimensional generalization of the deformed conifold. At the bottom of the warped throat there is a 4-sphere threaded by \( \tilde{M} \) units of 4-form flux. The dual (2 + 1)-dimensional theory has a discrete spectrum of bound states. We add p anti-M2 branes at a point on the 4-sphere, and show that they blow up into an M5-brane wrapping a 3-sphere at a fixed azimuthal angle on the 4-sphere. This supersymmetry breaking state turns out to be metastable for \( {{p} \left/ {{\tilde{M}}} \right.}\mathop { < }\limits_\sim 0.054 \). We find a smooth O(3)-symmetric Euclidean bounce solution in the M5-brane world volume theory that describes the decay of the false vacuum. Calculation of the Euclidean action shows that the metastable state is extremely long-lived. We also describe the corresponding metastable states and their decay in the type IIA background obtained by reduction along one of the spatial directions of \( {\mathbb{R}^{2,1}} \).
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References
N. Seiberg, Electric-magnetic duality in supersymmetric non-abelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [SPIRES].
K.A. Intriligator, N. Seiberg and D. Shih, Dynamical SUSY breaking in meta-stable vacua, JHEP 04 (2006) 021 [hep-th/0602239] [SPIRES].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [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].
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].
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].
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. Bena, M. Graña and N. Halmagyi, On the existence of meta-stable vacua in Klebanov-Strassler, JHEP 09 (2010) 087 [arXiv:0912.3519] [SPIRES].
R.C. Myers, Dielectric-branes, JHEP 12 (1999) 022 [hep-th/9910053] [SPIRES].
C. Bachas, M.R. Douglas and C. Schweigert, Flux stabilization of D-branes, JHEP 05 (2000) 048 [hep-th/0003037] [SPIRES].
B. Freivogel and M. Lippert, Evidence for a bound on the lifetime of de Sitter space, JHEP 12 (2008) 096 [arXiv:0807.1104] [SPIRES].
I.R. Klebanov and E. Witten, Superconformal field theory on threebranes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [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].
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].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N =6 superconformal Chern-Simons-matter theories, M 2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [SPIRES].
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].
M. Stenzel, Ricci-flat metrics on the complexification of a compact rank one symmetric space, Manuscripta Math. 80 (1993) 151.
P. Candelas and X.C. de la Ossa, Comments on conifolds, Nucl. Phys. B 342 (1990) 246 [SPIRES].
J. Lin, Bound state spectrum from gauge/gravity duality, Senior thesis, Princeton University, Princeton U.S.A. (2010).
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].
C.P. Herzog and I.R. Klebanov, Gravity duals of fractional branes in various dimensions, Phys. Rev. D 63 (2001) 126005 [hep-th/0101020] [SPIRES].
S.R. Coleman, The fate of the false vacuum. 1. Semiclassical theory, Phys. Rev. D 15 (1977) 2929 [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].
A. Hatcher, Algebraic topology, Cambridge University Press, Cambridge U.K. (2002).
C.P. Herzog, I.R. Klebanov and P. Ouyang, D-branes on the conifold and N =1 gauge/gravity dualities, hep-th/0205100 [SPIRES].
J. Polchinski, String theory. Volume 2: superstring theory and beyond, Cambridge University Press, Cambridge U.K. (1998).
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [SPIRES].
E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [SPIRES].
A. Dymarsky, I.R. Klebanov and N. Seiberg, On the moduli space of the cascading SU(M + p) × SU(p) gauge theory, JHEP 01 (2006) 155 [hep-th/0511254] [SPIRES].
C.G. Callan Jr., A. Guijosa and K.G. Savvidy, Baryons and string creation from the fivebrane worldvolume action, Nucl. Phys. B 547 (1999) 127 [hep-th/9810092] [SPIRES].
C.G. Callan Jr., A. Guijosa, K.G. Savvidy and O. Tafjord, Baryons and flux tubes in confining gauge theories from brane actions, Nucl. Phys. B 555 (1999) 183 [hep-th/9902197] [SPIRES].
C.P. Herzog, String tensions and three dimensional confining gauge theories, Phys. Rev. D 66 (2002) 065009 [hep-th/0205064] [SPIRES].
C.G. Callan Jr. and I.R. Klebanov, D-brane boundary state dynamics, Nucl. Phys. B 465 (1996) 473 [hep-th/9511173] [SPIRES].
S.S. Gubser, C.P. Herzog and I.R. Klebanov, Symmetry breaking and axionic strings in the warped deformed conifold, JHEP 09 (2004) 036 [hep-th/0405282] [SPIRES].
A. Basu and J.A. Harvey, The M2-M5 brane system and a generalized Nahm’s equation, Nucl. Phys. B 713 (2005) 136 [hep-th/0412310] [SPIRES].
A. Hashimoto, Comments on domain walls in holographic duals of mass deformed conformal field theories, JHEP 07 (2011) 031 [arXiv:1105.3687] [SPIRES].
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ArXiv ePrint:1006.3587
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Klebanov, I.R., Pufu, S.S. M-branes and metastable states. J. High Energ. Phys. 2011, 35 (2011). https://doi.org/10.1007/JHEP08(2011)035
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DOI: https://doi.org/10.1007/JHEP08(2011)035