Abstract
We study consistent Kaluza-Klein reductions of type IIB supergravity on T 1,1 down to five-dimensions. We find that the most general reduction containing singlets under the global SU(2) × SU(2) symmetry of T 1,1 is \( \mathcal{N} = 4 \) gauged supergravity coupled to three vector multiplets with a particular gauging due to topological and geometric flux. Key to this reduction is several modes which have not been considered before in the literature and our construction allows us to easily show that the Papadopoulos -Tseytlin ansatz for IIB solutions on T 1,1 is a consistent truncation. This explicit reduction provides an organizing principle for the linearized spectrum around the warped deformed conifold as well as the baryonic branch and should have applications to the physics of flux compactifications with warped throats.
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References
P. Candelas and X.C. de la Ossa, Comments on conifolds, Nucl. Phys. B 342 (1990) 246 [SPIRES].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [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].
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].
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] [SPIRES].
A.H. Chamseddine and M.S. Volkov, Non-abelian BPS monopoles in n =4 gauged supergravity, Phys. Rev. Lett. 79 (1997) 3343 [hep-th/9707176] [SPIRES].
J.M. Maldacena and C. Núñez, Towards the large-N limit of pure N =1 super Yang-Mills, Phys. Rev. Lett. 86 (2001) 588 [hep-th/0008001] [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].
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. Butti, M. Graña, R. Minasian, M. Petrini and A. Zaffaroni, The baryonic branch of Klebanov-Strassler solution: a supersymmetric family of SU(3) structure backgrounds, JHEP 03 (2005) 069 [hep-th/0412187] [SPIRES].
J. Maldacena and D. Martelli, The unwarped, resolved, deformed conifold: five branes and the baryonic branch of the Klebanov-Strassler theory, JHEP 01 (2010) 104 [arXiv:0906.0591] [SPIRES].
M. Berg, M. Haack and W. Mueck, Bulk dynamics in confining gauge theories, Nucl. Phys. B 736 (2006) 82 [hep-th/0507285] [SPIRES].
M. Berg, M. Haack and W. Mueck, Glueballs vs. gluinoballs: fluctuation spectra in non-AdS/non-CFT, Nucl. Phys. B 789 (2008) 1 [hep-th/0612224] [SPIRES].
A. Dymarsky and D. Melnikov, Gravity multiplet on KS and BB backgrounds, JHEP 05 (2008) 035 [arXiv:0710.4517] [SPIRES].
M.K. Benna, A. Dymarsky, I.R. Klebanov and A. Solovyov, On normal modes of a warped throat, JHEP 06 (2008) 070 [arXiv:0712.4404] [SPIRES].
A. Dymarsky, D. Melnikov and A. Solovyov, I-odd sector of the Klebanov-Strassler theory, JHEP 05 (2009) 105 [arXiv:0810.5666] [SPIRES].
I. Gordeli and D. Melnikov, On I-even singlet glueballs in the Klebanov-Strassler theory, arXiv:0912.5517 [SPIRES].
J.P. Gauntlett and O. Varela, Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions, Phys. Rev. D 76 (2007) 126007 [arXiv:0707.2315] [SPIRES].
J.P. Gauntlett, S. Kim, O. Varela and D. Waldram, Consistent supersymmetric Kaluza–Klein truncations with massive modes, JHEP 04 (2009) 102 [arXiv:0901.0676] [SPIRES].
D. Cassani, G. Dall’Agata and A.F. Faedo, Type IIB supergravity on squashed Sasaki-Einstein manifolds, JHEP 05 (2010) 094 [arXiv:1003.4283] [SPIRES].
J.P. Gauntlett and O. Varela, Universal Kaluza-Klein reductions of type IIB to N =4 supergravity in five dimensions, JHEP 06 (2010) 081 [arXiv:1003.5642] [SPIRES].
J.T. Liu, P. Szepietowski and Z. Zhao, Consistent massive truncations of IIB supergravity on Sasaki-Einstein manifolds, Phys. Rev. D 81 (2010) 124028 [arXiv:1003.5374] [SPIRES].
K. Skenderis, M. Taylor and D. Tsimpis, A consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure, JHEP 06 (2010) 025 [arXiv:1003.5657] [SPIRES].
C.P. Herzog, I.R. Klebanov, S.S. Pufu and T. Tesileanu, Emergent quantum near-criticality from baryonic black branes, JHEP 03 (2010) 093 [arXiv:0911.0400] [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].
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, 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].
C.N. Pope and N.P. Warner, An SU(4) invariant compactification of D = 11 supergravity on a stretched seven sphere, Phys. Lett. B 150 (1985) 352 [SPIRES].
N. Bobev, N. Halmagyi, K. Pilch and N.P. Warner, Supergravity instabilities of non-supersymmetric quantum critical points, Class. Quant. Grav. 27 (2010) 235013 [arXiv:1006.2546] [SPIRES].
D. Cassani and A.F. Faedo, A supersymmetric consistent truncation for conifold solutions, Nucl. Phys. B 843 (2011) 455 [arXiv:1008.0883] [SPIRES].
G. Dall’Agata, C. Herrmann and M. Zagermann, General matter coupled N =4 gauged supergravity in five dimensions, Nucl. Phys. B 612 (2001) 123 [hep-th/0103106] [SPIRES].
J. Schon and M. Weidner, Gauged N =4 supergravities, JHEP 05 (2006) 034 [hep-th/0602024] [SPIRES].
H. Samtleben, Lectures on gauged supergravity and flux compactifications, Class. Quant. Grav. 25 (2008) 214002 [arXiv:0808.4076] [SPIRES].
M. Awada and P.K. Townsend, N =4 Maxwell-Einstein supergravity in five-dimensions and its SU(2) gauging, Nucl. Phys. B 255 (1985) 617 [SPIRES].
H. Lü, C.N. Pope and K.S. Stelle, M-theory/heterotic duality: a Kaluza-Klein perspective, Nucl. Phys. B 548 (1999) 87 [hep-th/9810159] [SPIRES].
R. Corrado, M. Günaydin, N.P. Warner and M. Zagermann, Orbifolds and flows from gauged supergravity, Phys. Rev. D 65 (2002) 125024 [hep-th/0203057] [SPIRES].
N. Halmagyi, K. Pilch, C. Romelsberger and N.P. Warner, The complex geometry of holographic flows of quiver gauge theories, JHEP 09 (2006) 063 [hep-th/0406147] [SPIRES].
N. Halmagyi, Missing mirrors: type IIA supergravity on the resolved conifold, arXiv:1003.2121 [SPIRES].
R. Minasian and D. Tsimpis, On the geometry of non-trivially embedded branes, Nucl. Phys. B 572 (2000) 499 [hep-th/9911042] [SPIRES].
C.P. Herzog, I.R. Klebanov and P. Ouyang, Remarks on the warped deformed conifold, hep-th/0108101 [SPIRES].
J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [SPIRES].
J.H. Schwarz, Covariant field equations of chiral N =2 D = 10 supergravity, Nucl. Phys. B 226 (1983) 269 [SPIRES].
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Bena, I., Giecold, G., Graña, M. et al. Supersymmetric consistent truncations of IIB on T 1,1 . J. High Energ. Phys. 2011, 21 (2011). https://doi.org/10.1007/JHEP04(2011)021
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DOI: https://doi.org/10.1007/JHEP04(2011)021