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Gauntlett, Jerome P.; Martelli, Dario; Sparks, James

Toric geometry and the dual of \(\mathcal{I}\)-extremization. (English) Zbl 1416.81155

J. High Energy Phys. 2019, No. 6, Paper No. 140, 65 p. (2019).
Summary: We consider \(d=3\), \( \mathcal{N}=2 \) gauge theories arising on membranes sitting at the apex of an arbitrary toric Calabi-Yau 4-fold cone singularity that are then further compactified on a Riemann surface, \({\Sigma}_g\), with a topological twist that preserves two supersymmetries. If the theories flow to a superconformal quantum mechanics in the infrared, then they have a \(D=11\) supergravity dual of the form \(\mathrm{AdS}_2 \times Y_9\), with electric four-form flux and where \(Y_9\) is topologically a fibration of a Sasakian \(Y_7\) over \({\Sigma}_g\). These \(D=11\) solutions are also expected to arise as the near horizon limit of magnetically charged black holes in \(\mathrm{AdS}_4 \times Y_7\), with a Sasaki-Einstein metric on \(Y_7\). We show that an off-shell entropy function for the dual \(\mathrm{AdS}_2\) solutions may be computed using the toric data and Kähler class parameters of the Calabi-Yau 4-fold, that are encoded in a master volume, as well as a set of integers that determine the fibration of \(Y_7\) over \({\Sigma}_g\) and a Kähler class parameter for \({\Sigma}_g\). We also discuss the class of supersymmetric \(\mathrm{AdS}_3 \times Y_7\) solutions of type IIB supergravity with five-form flux only in the case that \(Y_7\) is toric, and show how the off-shell central charge of the dual field theory can be obtained from the toric data. We illustrate with several examples, finding agreement both with explicit supergravity solutions as well as with some known field theory results concerning \(\mathcal{I}\)-extremization.

Cited in 1 Review
Cited in 19 Documents

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83C57 Black holes
83E30 String and superstring theories in gravitational theory
81T60 Supersymmetric field theories in quantum mechanics
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
83E50 Supergravity

Keywords:

AdS-CFT correspondence; gauge-gravity correspondence; black holes in string theory; supersymmetric gauge theory
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\textit{J. P. Gauntlett} et al., J. High Energy Phys. 2019, No. 6, Paper No. 140, 65 p. (2019; Zbl 1416.81155)
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References:

[1] S.M. Hosseini and A. Zaffaroni, Large N matrix models for \[3dN=2 \mathcal{N}=2\] theories: twisted index, free energy and black holes, JHEP08 (2016) 064 [arXiv:1604.03122] [INSPIRE]. · Zbl 1390.83345
[2] K.A. Intriligator and B. Wecht, The Exact superconformal R symmetry maximizes a, Nucl. Phys.B 667 (2003) 183 [hep-th/0304128] [INSPIRE]. · Zbl 1059.81602
[3] F. Benini and N. Bobev, Exact two-dimensional superconformal R-symmetry and c-extremization, Phys. Rev. Lett.110 (2013) 061601 [arXiv:1211.4030] [INSPIRE]. · Zbl 1390.83325
[4] D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP05 (2012) 159 [arXiv:1012.3210] [INSPIRE]. · Zbl 1348.81420
[5] C. Couzens, J.P. Gauntlett, D. Martelli and J. Sparks, A geometric dual of c-extremization, JHEP01 (2019) 212 [arXiv:1810.11026] [INSPIRE]. · Zbl 1409.81143
[6] F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS4from supersymmetric localization, JHEP05 (2016) 054 [arXiv:1511.04085] [INSPIRE]. · Zbl 1388.83388
[7] A. Cabo-Bizet, V.I. Giraldo-Rivera and L.A. Pando Zayas, Microstate counting of AdS4hyperbolic black hole entropy via the topologically twisted index, JHEP08 (2017) 023 [arXiv:1701.07893] [INSPIRE]. · Zbl 1381.83055
[8] F. Azzurli, N. Bobev, P.M. Crichigno, V.S. Min and A. Zaffaroni, A universal counting of black hole microstates in AdS4, JHEP02 (2018) 054 [arXiv:1707.04257] [INSPIRE]. · Zbl 1387.81303
[9] F. Benini and A. Zaffaroni, Supersymmetric partition functions on Riemann surfaces, Proc. Symp. Pure Math.96 (2017) 13 [arXiv:1605.06120] [INSPIRE]. · Zbl 1430.81077
[10] D. Martelli, J. Sparks and S.-T. Yau, The Geometric dual of a-maximisation for Toric Sasaki-Einstein manifolds, Commun. Math. Phys.268 (2006) 39 [hep-th/0503183] [INSPIRE]. · Zbl 1190.53041
[11] D. Martelli, J. Sparks and S.-T. Yau, Sasaki-Einstein manifolds and volume minimisation, Commun. Math. Phys.280 (2008) 611 [hep-th/0603021] [INSPIRE]. · Zbl 1161.53029
[12] S. Giombi and I.R. Klebanov, Interpolating between a and F , JHEP03 (2015) 117 [arXiv:1409.1937] [INSPIRE]. · Zbl 1388.81383
[13] N. Kim, AdS3solutions of IIB supergravity from D3-branes, JHEP01 (2006) 094 [hep-th/0511029] [INSPIRE].
[14] N. Kim and J.-D. Park, Comments on AdS2solutions of D = 11 supergravity, JHEP09 (2006) 041 [hep-th/0607093] [INSPIRE].
[15] J.P. Gauntlett and N. Kim, Geometries with Killing Spinors and Supersymmetric AdS Solutions, Commun. Math. Phys.284 (2008) 897 [arXiv:0710.2590] [INSPIRE]. · Zbl 1179.53078
[16] J.P. Gauntlett, D. Martelli and J. Sparks, Toric geometry and the dual of c-extremization, JHEP01 (2019) 204 [arXiv:1812.05597] [INSPIRE]. · Zbl 1409.81118
[17] S.M. Hosseini and A. Zaffaroni, Proving the equivalence of c-extremization and its gravitational dual for all toric quivers, JHEP03 (2019) 108 [arXiv:1901.05977] [INSPIRE]. · Zbl 1414.81208
[18] J.P. Gauntlett, O.A.P. Mac Conamhna, T. Mateos and D. Waldram, Supersymmetric AdS3solutions of type IIB supergravity, Phys. Rev. Lett.97 (2006) 171601 [hep-th/0606221] [INSPIRE]. · Zbl 1228.83112
[19] S.M. Hosseini, K. Hristov and A. Passias, Holographic microstate counting for AdS4black holes in massive IIA supergravity, JHEP10 (2017) 190 [arXiv:1707.06884] [INSPIRE]. · Zbl 1383.83212
[20] F. Benini, H. Khachatryan and P. Milan, Black hole entropy in massive Type IIA, Class. Quant. Grav.35 (2018) 035004 [arXiv:1707.06886] [INSPIRE]. · Zbl 1382.83040
[21] N. Bobev, V.S. Min and K. Pilch, Mass-deformed ABJM and black holes in AdS4, JHEP03 (2018) 050 [arXiv:1801.03135] [INSPIRE]. · Zbl 1388.83752
[22] M. Suh, Supersymmetric AdS6black holes from F (4) gauged supergravity, JHEP01 (2019) 035 [arXiv:1809.03517] [INSPIRE]. · Zbl 1409.83214
[23] S.M. Hosseini, K. Hristov, A. Passias and A. Zaffaroni, 6D attractors and black hole microstates, arXiv:1809.10685 [INSPIRE]. · Zbl 1405.83074
[24] M. Suh, Supersymmetric AdS6black holes from matter coupled F (4) gauged supergravity, JHEP02 (2019) 108 [arXiv:1810.00675] [INSPIRE]. · Zbl 1411.83139
[25] J.P. Gauntlett, D. Martelli, J. Sparks and S.-T. Yau, Obstructions to the existence of Sasaki-Einstein metrics, Commun. Math. Phys.273 (2007) 803 [hep-th/0607080] [INSPIRE]. · Zbl 1149.53026
[26] A. Futaki, H. Ono and G. Wang, Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds, J. Diff. Geom.83 (2009) 585 [math/0607586] [INSPIRE]. · Zbl 1188.53042
[27] J.P. Gauntlett, O.A.P. Mac Conamhna, T. Mateos and D. Waldram, New supersymmetric AdS3solutions, Phys. Rev.D 74 (2006) 106007 [hep-th/0608055] [INSPIRE]. · Zbl 1228.83112
[28] J.P. Gauntlett, N. Kim and D. Waldram, Supersymmetric AdS3, AdS2and Bubble Solutions, JHEP04 (2007) 005 [hep-th/0612253] [INSPIRE].
[29] S.M. Hosseini and N. Mekareeya, Large N topologically twisted index: necklace quivers, dualities and Sasaki-Einstein spaces, JHEP08 (2016) 089 [arXiv:1604.03397] [INSPIRE]. · Zbl 1390.81600
[30] S.M. Hosseini and A. Zaffaroni, Geometry of ℐ-extremization and black holes microstates, arXiv:1904.04269 [INSPIRE]. · Zbl 1418.83026
[31] D. Martelli and J. Sparks, Notes on toric Sasaki-Einstein seven-manifolds and AdS4/CF T3, JHEP11 (2008) 016 [arXiv:0808.0904] [INSPIRE].
[32] A. Hanany, D. Vegh and A. Zaffaroni, Brane Tilings and M2 Branes, JHEP03 (2009) 012 [arXiv:0809.1440] [INSPIRE].
[33] J.P. Gauntlett, S. Kim and D. Waldram, unpublished notes (2008).
[34] J.P. Gauntlett, D. Martelli, J.F. Sparks and D. Waldram, A New infinite class of Sasaki-Einstein manifolds, Adv. Theor. Math. Phys.8 (2004) 987 [hep-th/0403038] [INSPIRE]. · Zbl 1095.53034
[35] D. Martelli and J. Sparks, Toric geometry, Sasaki-Einstein manifolds and a new infinite class of AdS/CFT duals, Commun. Math. Phys.262 (2006) 51 [hep-th/0411238] [INSPIRE]. · Zbl 1112.53034
[36] L.J. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, Nucl. Phys.B 383 (1992) 395 [hep-th/9203018] [INSPIRE].
[37] M.M. Caldarelli and D. Klemm, Supersymmetry of Anti-de Sitter black holes, Nucl. Phys.B 545 (1999) 434 [hep-th/9808097] [INSPIRE]. · Zbl 0953.83020
[38] J.P. Gauntlett, N. Kim, S. Pakis and D. Waldram, Membranes wrapped on holomorphic curves, Phys. Rev.D 65 (2002) 026003 [hep-th/0105250] [INSPIRE].
[39] J.P. Gauntlett and O. Varela, Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions, Phys. Rev.D 76 (2007) 126007 [arXiv:0707.2315] [INSPIRE]. · Zbl 1181.83184
[40] C. Couzens, D. Martelli and S. Schäfer-Nameki, F-theory and AdS3/CF T2 (2, 0), JHEP06 (2018) 008 [arXiv:1712.07631] [INSPIRE]. · Zbl 1395.81211
[41] C.P. Herzog, I.R. Klebanov, S.S. Pufu and T. Tesileanu, Multi-Matrix Models and Tri-Sasaki Einstein Spaces, Phys. Rev.D 83 (2011) 046001 [arXiv:1011.5487] [INSPIRE].
[42] D. Martelli and J. Sparks, The large N limit of quiver matrix models and Sasaki-Einstein manifolds, Phys. Rev.D 84 (2011) 046008 [arXiv:1102.5289] [INSPIRE].
[43] S. Cheon, H. Kim and N. Kim, Calculating the partition function of N = 2 Gauge theories on S3and AdS/CFT correspondence, JHEP05 (2011) 134 [arXiv:1102.5565] [INSPIRE]. · Zbl 1296.81055
[44] D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-Theorem: N = 2 Field Theories on the Three-Sphere, JHEP06 (2011) 102 [arXiv:1103.1181] [INSPIRE]. · Zbl 1298.81304
[45] F. Benini and A. Zaffaroni, A topologically twisted index for three-dimensional supersymmetric theories, JHEP07 (2015) 127 [arXiv:1504.03698] [INSPIRE]. · Zbl 1388.81400
[46] D. Berenstein, C.P. Herzog and I.R. Klebanov, Baryon spectra and AdS/CF T correspondence, JHEP06 (2002) 047 [hep-th/0202150] [INSPIRE].
[47] F. Benini, C. Closset and S. Cremonesi, Chiral flavors and M2-branes at toric CY4 singularities, JHEP02 (2010) 036 [arXiv:0911.4127] [INSPIRE]. · Zbl 1270.81151
[48] D. Farquet and J. Sparks, Wilson loops and the geometry of matrix models in AdS4/CF T3, JHEP01 (2014) 083 [arXiv:1304.0784] [INSPIRE].
[49] S. Franco, A. Hanany, D. Martelli, J. Sparks, D. Vegh and B. Wecht, Gauge theories from toric geometry and brane tilings, JHEP01 (2006) 128 [hep-th/0505211] [INSPIRE].
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