Superconformal symmetry in the Kaluza-Klein spectrum of warped \(\mathrm{AdS}(3)\). (English) Zbl 1390.83316
Summary: We study the Kaluza-Klein spectrum of warped \(\mathrm{AdS}_3\) compactifications of type IIB with five-form flux which are dual to \(\mathcal N=(0,2)\) SCFTs in two dimensions. We prove that the spectra of fluctuations of both the spin 2 sector of the graviton and the axio-dilaton are bounded. At the bound the modes have the correct quantum numbers to be chiral primaries and descendants thereof respectively. Moreover, we prove that the same modes give rise to superpartners in the dilatino spectrum. Our results show that a subset of the mesonic chiral ring of the dual SCFT is isomorphic to the first Kohn-Rossi cohomology groups. As an example, we consider the compactification of four-dimensional \(Y^{p,q}\) theories on Riemann surfaces for the case of the universal twist. We conclude by studying fluctuations of the three-form, where we are able to identify Betti multiplets after imposing some mild assumptions.
References:
| [1] | Kim, HJ; Romans, LJ; Nieuwenhuizen, P., the mass spectrum of chiral N = 2 \(D\)=10 supergravity on S\^{}{5}, Phys. Rev., D 32, 389, (1985) |
| [2] | Ceresole, A.; Dall’Agata, G.; D’Auria, R., KK spectroscopy of type IIB supergravity on AdS_{5} × \(T\)\^{}{11}, JHEP, 11, 009, (1999) · Zbl 0955.83041 · doi:10.1088/1126-6708/1999/11/009 |
| [3] | Ceresole, A.; Dall’Agata, G.; D’Auria, R.; Ferrara, S., spectrum of type IIB supergravity on AdS_{5} × \(T\)\^{}{1}1: predictions on N = 1 SCFT’s, Phys. Rev., D 61, 066001, (2000) · Zbl 0952.81047 |
| [4] | Deger, S.; Kaya, A.; Sezgin, E.; Sundell, P., spectrum of D = 6, N = 4b supergravity on AdS in three-dimensions ×\(S\)\^{}{3}, Nucl. Phys., B 536, 110, (1998) · Zbl 0940.83030 · doi:10.1016/S0550-3213(98)00555-0 |
| [5] | Boer, J., six-dimensional supergravity on S\^{}{3} × AdS_{3}and 2D conformal field theory, Nucl. Phys., B 548, 139, (1999) · Zbl 0944.83032 · doi:10.1016/S0550-3213(99)00160-1 |
| [6] | Merlatti, P., M theory on AdS_{4} × \(Q\)\^{}{111}: the complete osp(2|4) × SU(2) × SU(2) × SU(2) spectrum from harmonic analysis, Class. Quant. Grav., 18, 2797, (2001) · Zbl 0994.83052 · doi:10.1088/0264-9381/18/14/312 |
| [7] | Fabbri, D.; Fré, P.; Gualtieri, L.; Termonia, P., M theory on AdS_{4} × \(M\)\^{}{111}: the complete osp(2|4) × SU(3) × SU(2) spectrum from harmonic analysis, Nucl. Phys., B 560, 617, (1999) · Zbl 0953.83036 · doi:10.1016/S0550-3213(99)00363-6 |
| [8] | Eager, R.; Schmude, J.; Tachikawa, Y., Superconformal indices, Sasaki-Einstein manifolds and cyclic homologies, Adv. Theor. Math. Phys., 18, 129, (2014) · Zbl 1309.81242 · doi:10.4310/ATMP.2014.v18.n1.a3 |
| [9] | Eager, R.; Schmude, J., superconformal indices and M 2-branes, JHEP, 12, 062, (2015) · Zbl 1388.83795 · doi:10.1007/JHEP12(2015)062 |
| [10] | Schmude, J., Laplace operators on Sasaki-Einstein manifolds, JHEP, 04, 008, (2014) · Zbl 1333.83012 · doi:10.1007/JHEP04(2014)008 |
| [11] | Klebanov, IR; Pufu, SS; Rocha, FD, The squashed, stretched and warped gets perturbed, JHEP, 06, 019, (2009) · doi:10.1088/1126-6708/2009/06/019 |
| [12] | Ahn, C.; Woo, K., perturbing around a warped product of AdS_{4}and seven-ellipsoid, JHEP, 08, 065, (2009) · doi:10.1088/1126-6708/2009/08/065 |
| [13] | Bachas, C.; Estes, J., Spin-2 spectrum of defect theories, JHEP, 06, 005, (2011) · Zbl 1298.81207 · doi:10.1007/JHEP06(2011)005 |
| [14] | A. Passias and A. Tomasiello, Spin-2 spectrum of six-dimensional field theories, arXiv:1604.04286 [INSPIRE]. · Zbl 1390.83127 |
| [15] | Pang, Y.; Rong, J., evidence for the holographic dual of\( \mathcal{N} \) = 3 solution in massive type IIA, Phys. Rev., D 93, 065038, (2016) |
| [16] | H. Larsson, Kaluza-Klein mass spectra, p-branes and AdS/CFT, Master thesis, Linköping University, Göeborg, Sweden (2000). |
| [17] | Bailin, D.; Love, A., Kaluza-Klein theories, Rept. Prog. Phys., 50, 1087, (1987) · doi:10.1088/0034-4885/50/9/001 |
| [18] | Duff, MJ; Nilsson, BEW; Pope, CN, Kaluza-Klein supergravity, Phys. Rept., 130, 1, (1986) · Zbl 0588.53073 · doi:10.1016/0370-1573(86)90163-8 |
| [19] | Kim, N., AdS_{3}solutions of IIB supergravity from D3-branes, JHEP, 01, 094, (2006) · doi:10.1088/1126-6708/2006/01/094 |
| [20] | Gauntlett, JP; Mac Conamhna, OAP; Mateos, T.; Waldram, D., supersymmetric AdS_{3}solutions of type IIB supergravity, Phys. Rev. Lett., 97, 171601, (2006) · Zbl 1228.83112 · doi:10.1103/PhysRevLett.97.171601 |
| [21] | Gauntlett, JP; Kim, N.; Waldram, D., supersymmetric AdS_{3}, AdS_{2}and bubble solutions, JHEP, 04, 005, (2007) · doi:10.1088/1126-6708/2007/04/005 |
| [22] | Gauntlett, JP; Mac Conamhna, OAP; Mateos, T.; Waldram, D., new supersymmetric AdS_{3}solutions, Phys. Rev., D 74, 106007, (2006) |
| [23] | Gauntlett, JP; Mac Conamhna, OAP, AdS spacetimes from wrapped D3-branes, Class. Quant. Grav., 24, 6267, (2007) · Zbl 1133.83012 · doi:10.1088/0264-9381/24/24/009 |
| [24] | Gauntlett, JP; Kim, N., Geometries with Killing spinors and supersymmetric AdS solutions, Commun. Math. Phys., 284, 897, (2008) · Zbl 1179.53078 · doi:10.1007/s00220-008-0575-5 |
| [25] | Martelli, D.; Sparks, J.; Yau, S-T, Sasaki-Einstein manifolds and volume minimisation, Commun. Math. Phys., 280, 611, (2008) · Zbl 1161.53029 · doi:10.1007/s00220-008-0479-4 |
| [26] | Sparks, J., Sasaki-Einstein manifolds, Surveys Diff. Geom., 16, 265, (2011) · Zbl 1256.53037 · doi:10.4310/SDG.2011.v16.n1.a6 |
| [27] | Benini, F.; Bobev, N.; Crichigno, PM, two-dimensional SCFTs from D3-branes, JHEP, 07, 020, (2016) · Zbl 1390.83088 · doi:10.1007/JHEP07(2016)020 |
| [28] | Benini, F.; Bobev, N., Two-dimensional SCFTs from wrapped branes and c-extremization, JHEP, 06, 005, (2013) · Zbl 1390.83325 · doi:10.1007/JHEP06(2013)005 |
| [29] | Donos, A.; Gauntlett, JP; Sparks, J., AdS_{3} × (\(S\)\^{}{3} × \(S\)\^{}{3} × \(S\)\^{}{1}) solutions of type IIB string theory, Class. Quant. Grav., 26, 065009, (2009) · Zbl 1162.83365 · doi:10.1088/0264-9381/26/6/065009 |
| [30] | Harvey, FR; Lawson, HB, Boundaries of complex analytic varieties, Bull. AMS, 80, 180, (1974) · Zbl 0281.32006 · doi:10.1090/S0002-9904-1974-13409-9 |
| [31] | Harvey, FR; Lawson, HB, On boundaries of complex analytic varieties, I, Ann. Math., 102, 223, (1975) · Zbl 0317.32017 · doi:10.2307/1971032 |
| [32] | Yau, SST, Kohn-rossi cohomology and its application to the complex plateau problem, I, Ann. Math., 113, 67, (1981) · Zbl 0464.32012 · doi:10.2307/1971134 |
| [33] | Bars, I.; Günaydin, M., Unitary representations of noncompact supergroups, Commun. Math. Phys., 91, 31, (1983) · Zbl 0531.17002 · doi:10.1007/BF01206048 |
| [34] | Günaydin, M.; Sierra, G.; Townsend, PK, the unitary supermultiplets of d = 3 anti-de Sitter and d = 2 conformal superalgebras, Nucl. Phys., B 274, 429, (1986) · doi:10.1016/0550-3213(86)90293-2 |
| [35] | Lerche, W.; Vafa, C.; Warner, NP, chiral rings in N = 2 superconformal theories, Nucl. Phys., B 324, 427, (1989) · doi:10.1016/0550-3213(89)90474-4 |
| [36] | Adams, A.; Distler, J.; Ernebjerg, M., Topological heterotic rings, Adv. Theor. Math. Phys., 10, 657, (2006) · Zbl 1116.81049 · doi:10.4310/ATMP.2006.v10.n5.a2 |
| [37] | D’Auria, R.; Fré, P., Universal Bose-Fermi mass relations in Kaluza-Klein supergravity and harmonic analysis on coset manifolds with Killing spinors, Annals Phys., 162, 372, (1985) · doi:10.1016/0003-4916(85)90166-6 |
| [38] | Pope, CN, Kähler manifolds and quantum gravity, J. Phys., A 15, 2455, (1982) · Zbl 0491.53051 |
| [39] | Arabi Ardehali, A.; Liu, JT; Szepietowski, P., The shortened KK spectrum of IIB supergravity on Y \^{}{p, q}, JHEP, 02, 064, (2014) · Zbl 1333.83207 · doi:10.1007/JHEP02(2014)064 |
| [40] | Gauntlett, JP; Martelli, D.; Sparks, J.; Waldram, D., Sasaki-Einstein metrics on S\^{}{2} × \(S\)\^{}{3}, Adv. Theor. Math. Phys., 8, 711, (2004) · Zbl 1136.53317 · doi:10.4310/ATMP.2004.v8.n4.a3 |
| [41] | Berenstein, D.; Herzog, CP; Ouyang, P.; Pinansky, S., Supersymmetry breaking from a Calabi-Yau singularity, JHEP, 09, 084, (2005) · doi:10.1088/1126-6708/2005/09/084 |
| [42] | Kihara, H.; Sakaguchi, M.; Yasui, Y., Scalar Laplacian on Sasaki-Einstein manifolds Y \^{}{p, q}, Phys. Lett., B 621, 288, (2005) · Zbl 1247.53053 · doi:10.1016/j.physletb.2005.06.061 |
| [43] | Oota, T.; Yasui, Y., Toric Sasaki-Einstein manifolds and Heun equations, Nucl. Phys., B 742, 275, (2006) · Zbl 1214.53041 · doi:10.1016/j.nuclphysb.2006.03.003 |
| [44] | Maldacena, JM; Strominger, A., AdS_{3}black holes and a stringy exclusion principle, JHEP, 12, 005, (1998) · Zbl 0951.83019 · doi:10.1088/1126-6708/1998/12/005 |
| [45] | Boer, J., Large-N elliptic genus and AdS/CFT correspondence, JHEP, 05, 017, (1999) · Zbl 1017.81041 · doi:10.1088/1126-6708/1999/05/017 |
| [46] | Aharony, O.; Gubser, SS; Maldacena, JM; Ooguri, H.; Oz, Y., Large-N field theories, string theory and gravity, Phys. Rept., 323, 183, (2000) · Zbl 1368.81009 · doi:10.1016/S0370-1573(99)00083-6 |
| [47] | Behrndt, K.; Bergshoeff, E.; Janssen, B., Intersecting D-branes in ten-dimensions and six-dimensions, Phys. Rev., D 55, 3785, (1997) |
| [48] | Gauntlett, JP; Kastor, DA; Traschen, JH, Overlapping branes in M-theory, Nucl. Phys., B 478, 544, (1996) · Zbl 0925.81199 · doi:10.1016/0550-3213(96)00423-3 |
| [49] | Eager, R., Superconformal field theories and cyclic homology, Proc. Symp. Pure Math., 93, 141, (2015) · Zbl 1359.81158 |
| [50] | A.F. Beardon, The geometry of discrete groups, Graduate Texts in Mathematics volume 91, Springer, Berlin Germany (2012). |
| [51] | Donos, A.; Gauntlett, JP; Kim, N., AdS solutions through transgression, JHEP, 09, 021, (2008) · Zbl 1245.83060 · doi:10.1088/1126-6708/2008/09/021 |
| [52] | Schwarz, JH, covariant field equations of chiral N = 2 \(D\) = 10 supergravity, Nucl. Phys., B 226, 269, (1983) · doi:10.1016/0550-3213(83)90192-X |
| [53] | DeWolfe, O.; Giddings, SB, Scales and hierarchies in warped compactifications and brane worlds, Phys. Rev., D 67, 066008, (2003) · Zbl 1222.83165 |
| [54] | Argurio, R.; Ferretti, G.; Petersson, C., Massless fermionic bound states and the gauge/gravity correspondence, JHEP, 03, 043, (2006) · Zbl 1226.81089 · doi:10.1088/1126-6708/2006/03/043 |
| [55] | Gubser, SS; Klebanov, IR, baryons and domain walls in an N = 1 superconformal gauge theory, Phys. Rev., D 58, 125025, (1998) |
| [56] | Berenstein, D.; Herzog, CP; Klebanov, IR, Baryon spectra and AdS/CFT correspondence, JHEP, 06, 047, (2002) · doi:10.1088/1126-6708/2002/06/047 |
| [57] | Gubser, SS; Klebanov, IR; Tseytlin, AA, String theory and classical absorption by three-branes, Nucl. Phys., B 499, 217, (1997) · Zbl 0959.81071 · doi:10.1016/S0550-3213(97)00325-8 |
| [58] | Constable, NR; Myers, RC, Spin two glueballs, positive energy theorems and the AdS/CFT correspondence, JHEP, 10, 037, (1999) · Zbl 0957.81095 · doi:10.1088/1126-6708/1999/10/037 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
