Resolved Calabi-Yau cones and flows from \(L^{abc}\) superconformal field theories. (English) Zbl 1150.81018
Summary: We discuss D3-branes on cohomogeneity-three resolved Calabi-Yau cones over \(L^{abc}\) spaces, for which a 2-cycle or 4-cycle has been blown up. In terms of the dual quiver gauge theory, this corresponds to motion along the non-mesonic, or baryonic, directions in the moduli space of vacua. In particular, a dimension-two and/or dimension-six scalar operator gets a vacuum expectation value. These resolved cones support various harmonic (2,1)-forms which reduce the ranks of some of the gauge groups either by a Seiberg duality cascade or by Higgsing. We also discuss higher-dimensional resolved Calabi-Yau cones. In particular, we obtain square-integrable (2,2)-forms for eight-dimensional cohomogeneity-four Calabi-Yau metrics.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 32Q25 | Calabi-Yau theory (complex-analytic aspects) |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
References:
| [1] | Maldacena, J. M., Int. J. Theor. Phys., 38, 1113 (1999) · Zbl 0969.81047 |
| [2] | Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M., Gauge theory correlators from non-critical string theory, Phys. Lett. B, 428, 105 (1998) · Zbl 1355.81126 |
| [3] | Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253 (1998) · Zbl 0914.53048 |
| [4] | Gauntlett, J. P.; Martelli, D.; Sparks, J.; Waldram, D., Supersymmetric \(AdS_5\) solutions of M-theory, Class. Quantum Grav., 21, 4335 (2004) · Zbl 1059.83038 |
| [5] | Gauntlett, J. P.; Martelli, D.; Sparks, J.; Waldram, D., Sasaki-Einstein metrics on \(S^2 \times S^3\), Adv. Theor. Math. Phys., 8, 711 (2004) · Zbl 1136.53317 |
| [6] | Cvetič, M.; Lü, H.; Page, D. N.; Pope, C. N., New Einstein-Sasaki spaces in five and higher dimensions, Phys. Rev. Lett., 95, 071101 (2005) |
| [7] | Cvetič, M.; Lü, H.; Page, D. N.; Pope, C. N., New Einstein-Sasaki and Einstein spaces from Kerr-de Sitter |
| [8] | Klebanov, I. R.; Witten, E., Superconformal field theory on threebranes at a Calabi-Yau singularity, Nucl. Phys. B, 536, 199 (1998) · Zbl 0948.81619 |
| [9] | Martelli, D.; Sparks, J., Toric geometry, Sasaki-Einstein manifolds and a new infinite class of AdS/CFT duals, Commun. Math. Phys., 262, 51 (2006) · Zbl 1112.53034 |
| [10] | Benvenuti, S.; Franco, S.; Hanany, A.; Martelli, D.; Sparks, J., An infinite family of superconformal quiver gauge theories with Sasaki-Einstein duals, JHEP, 0506, 064 (2005) |
| [11] | Benvenuti, S.; Kruczenski, M., From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr, JHEP, 0604, 033 (2006) |
| [12] | Franco, S.; Hanany, A.; Martelli, D.; Sparks, J.; Vegh, D.; Wecht, B., Gauge theories from toric geometry and brane tilings, JHEP, 0601, 128 (2006) |
| [13] | Butti, A.; Forcella, D.; Zaffaroni, A., The dual superconformal theory for \(L^{p q r}\) manifolds, JHEP, 0509, 018 (2005) |
| [14] | Klebanov, I. R.; Witten, E., AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B, 556, 89 (1999) · Zbl 0958.81134 |
| [15] | Pando Zayas, L. A.; Tseytlin, A. A., 3-branes on spaces with \(R \times S^2 \times S^3\) topology, Phys. Rev. D, 63, 086006 (2001) |
| [16] | Pal, S. S., A new Ricci flat geometry, Phys. Lett. B, 614, 201 (2005) · Zbl 1247.53056 |
| [17] | Sfetsos, K.; Zoakos, D., Supersymmetric solutions based on \(Y^{p q}\) and \(L^{p q r}\), Phys. Lett. B, 625, 135 (2005) · Zbl 1247.53057 |
| [18] | Benvenuti, S.; Mahato, M.; Pando Zayas, L. A.; Tachikawa, Y., The gauge/gravity theory of blown up four cycles |
| [19] | Berard-Bergery, L., Quelques exemples de varietes riemanniennes completes non compactes a courbure de Ricci positive, C. R. Acad. Sci. Paris, Ser. I, 302, 159 (1986) · Zbl 0585.53033 |
| [20] | Page, D. N.; Pope, C. N., Inhomogeneous Einstein metrics on complex line bundles, Class. Quantum Grav., 4, 213 (1987) · Zbl 0613.53020 |
| [21] | Chen, W.; Lü, H.; Pope, C. N., Kerr-de Sitter black holes with NUT charges, Nucl. Phys. B, 762, 38 (2007) · Zbl 1116.83015 |
| [22] | Chen, W.; Lü, H.; Pope, C. N., General Kerr-NUT-AdS metrics in all dimensions, Class. Quantum Grav., 23, 5323 (2006) · Zbl 1100.83006 |
| [23] | Lü, H.; Pope, C. N.; Vazquez-Poritz, J. F., A new construction of Einstein-Sasaki metrics in \(D \geqslant 7\), Phys. Rev. D, 75, 026005 (2007) |
| [24] | Oota, T.; Yasui, Y., Explicit toric metric on resolved Calabi-Yau cone, Phys. Lett. B, 639, 54 (2006) · Zbl 1248.83144 |
| [25] | Lü, H.; Pope, C. N., Resolutions of cones over Einstein-Sasaki spaces · Zbl 1188.53044 |
| [26] | Klebanov, I. R.; Murugan, A., Gauge/gravity duality and warped resolved conifold |
| [27] | Klebanov, I. R.; Nekrasov, N. A., Gravity duals of fractional branes and logarithmic RG flow, Nucl. Phys. B, 574, 263 (2000) · Zbl 1056.81553 |
| [28] | Klebanov, I. R.; Tseytlin, A. A., Gravity duals of supersymmetric \(SU(N) \times SU(N + M)\) gauge theories, Nucl. Phys. B, 578, 123 (2000) · Zbl 0976.81109 |
| [29] | Herzog, C. P.; Ejaz, Q. J.; Klebanov, I. R., Cascading RG flows from new Sasaki-Einstein manifolds, JHEP, 0502, 009 (2005) |
| [30] | Martelli, D.; Sparks, J., Toric Sasaki-Einstein metrics on \(S^2 \times S^3\), Phys. Lett. B, 621, 208 (2005) · Zbl 1247.53055 |
| [31] | Gepner, D.; Pal, S. S., Branes in \(L^{p q r}\), Phys. Lett. B, 622, 136 (2005) |
| [32] | Klebanov, I. R.; Strassler, M. J., Supergravity and a confining gauge theory: Duality cascades and \(χ\) SB-resolution of naked singularities, JHEP, 0008, 052 (2000) · Zbl 0986.83041 |
| [33] | Pando Zayas, L. A.; Tseytlin, A. A., 3-branes on resolved conifold, JHEP, 0011, 028 (2000) · Zbl 0990.81603 |
| [34] | Aharony, O., A note on the holographic interpretation of string theory backgrounds with varying flux, JHEP, 0103, 012 (2001) |
| [35] | Candelas, P.; de la Ossa, X. C., Comments on conifolds, Nucl. Phys. B, 342, 246 (1990) |
| [36] | Burrington, B. A.; Liu, J. T.; Mahato, M.; Pando Zayas, L. A., Towards supergravity duals of chiral symmetry breaking in Sasaki-Einstein cascading quiver theories, JHEP, 0507, 019 (2005) |
| [37] | Altmann, K., The versal deformation of an isolated toric Gorenstein singularity · Zbl 0894.14025 |
| [38] | Altmann, K., Infinitesimal deformations and obstructions for toric singularities · Zbl 0922.14035 |
| [39] | Berenstein, D.; Herzog, C. P.; Ouyang, P.; Pinansky, S., Supersymmetry breaking from a Calabi-Yau singularity, JHEP, 0509, 084 (2005) |
| [40] | Franco, S.; Hanany, A.; Saad, F.; Uranga, A. M., Fractional branes and dynamical supersymmetry breaking, JHEP, 0601, 011 (2006) |
| [41] | Bertolini, M.; Bigazzi, F.; Cotrone, A. L., Supersymmetry breaking at the end of a cascade of Seiberg dualities, Phys. Rev. D, 72, 061902 (2005) |
| [42] | Brini, A.; Forcella, D., Comments on the non-conformal gauge theories dual to \(Y^{p q}\) manifolds, JHEP, 0606, 050 (2006) |
| [43] | Page, D. N.; Kubizňák, D.; Vasudevan, M.; Krtouš, P., Complete integrability of geodesic motion in general Kerr-NUT-AdS spacetimes, Phys. Rev. Lett., 98, 061102 (2007) · Zbl 1228.83075 |
| [44] | Frolov, V. P.; Krtouš, P.; Kubizňák, D., Separability of Hamilton-Jacobi and Klein-Gordon equations in general Kerr-NUT-AdS spacetimes, JHEP, 0702, 005 (2007) |
| [45] | Krtouš, P.; Kubizňák, D.; Page, D. N.; Frolov, V. P., Killing-Yano tensors, rank-2 Killing tensors and conserved quantities in higher dimensions, JHEP, 0702, 004 (2007) |
| [46] | Lü, H.; Vázquez-Poritz, J. F., \(S^1\)-wrapped D3-branes on conifolds, Nucl. Phys. B, 633, 114 (2002) · Zbl 0995.81093 |
| [47] | P. Argyres, M. Edalati, J.F. Vázquez-Poritz, in preparation; P. Argyres, M. Edalati, J.F. Vázquez-Poritz, in preparation |
| [48] | Lunin, O.; Maldacena, L., Deforming field theories with \(U(1) \times U(1)\) global symmetry and their gravity duals, JHEP, 0505, 033 (2005) |
| [49] | Cvetič, M.; Lü, H.; Pope, C. N., Brane resolution through transgression, Nucl. Phys. B, 600, 103 (2001) · Zbl 1043.81647 |
| [50] | Cvetič, M.; Gibbons, G. W.; Lü, H.; Pope, C. N., Ricci-flat metrics, harmonic forms and brane resolutions, Commun. Math. Phys., 232, 457 (2003) · Zbl 1027.53044 |
| [51] | Cvetič, M.; Gibbons, G. W.; Lü, H.; Pope, C. N., Hyper-Kähler Calabi metrics, \(L^2\) harmonic forms, resolved M2-branes, and \(AdS_4/CFT_3\) correspondence, Nucl. Phys. B, 617, 151 (2001) · Zbl 0990.53046 |
| [52] | Ahn, C.; Vázquez-Poritz, J. F., Marginal deformations with \(U(1)^3\) global symmetry, JHEP, 0507, 032 (2005) |
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