F-theory and \(\mathrm{AdS}_3 /\mathrm{CFT}_2 (2,0)\). (English) Zbl 1395.81211

Couzens, Christopher; Martelli, Dario; Schäfer-Nameki, Sakura

J. High Energy Phys. 2018, No. 6, Paper No. 8, 98 p. (2018).

Summary: We continue to develop the program initiated in [the authors et al., J. High Energy Phys. 2017, No. 8, Paper No. 43, 72 p. (2017; Zbl 1381.81110)] of studying supersymmetric \(\mathrm{AdS}_{3}\) backgrounds of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of theories with varying coupling. Imposing 2d \( \mathcal{N}=\left(0,2\right) \) supersymmetry, we derive the general conditions on the geometry for TypeIIB \(\mathrm{AdS}_{3}\) solutions with varying axio-dilaton and five-form flux. Locally the compact part of spacetime takes the form of a circle fibration over an eight-fold \( {\mathcal{Y}}_8^{\tau} \), which is elliptically fibered over a base \( {\tilde{\mathcal{M}}}_6 \). We construct two classes of solutions given in terms of a product ansatz \( \tilde{\mathcal{M}}_6 = \Sigma \times {M}_4 \), where \(\Sigma\) is a complex curve and \( {\tilde{\mathcal{M}}}_4 \) is locally a Kähler surface. In the first class \( {\tilde{ \mathcal{M}}}_4 \) is globally a Kähler surface and we take the elliptic fibration to vary non-trivially over either of these two factors, where in both cases the metrics on the total space of the elliptic fibrations are not Ricci-flat. In the second class the metric on the total space of the \(\mathrm{AdS}_{3} \times \mathrm{K3} \times \mathcal{M}_5^{\tau}\), dual to 2d (0, 2) SCFTs, and \( \mathrm{AdS}_{3} \times S^3 / \Gamma \times CY_{3} \), dual to 2d (0, 4) SCFTs, respectively. In all cases we compute the charges for the dual field theories with varying coupling and find agreement with the holographic results. We also show that solutions with enhanced 2d \( \mathcal{N}=\left(2,2\right) \) supersymmetry must have constant axio-dilaton. Allowing the internal geometry to be non-compact leads to the most general class of Type IIB \(\mathrm{AdS}_{5}\) solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d \( \mathcal{N}=1 \) SCFTs.

MSC:

81T40	Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T60	Supersymmetric field theories in quantum mechanics
53B35	Local differential geometry of Hermitian and Kählerian structures
83C15	Exact solutions to problems in general relativity and gravitational theory

Keywords:

AdS-CFT correspondence; F-theory

Citations:

Zbl 1381.81110

References:

[1]	Couzens, C.; etal., F-theory and ads_{3}/CFT_{2}, JHEP, 08, 043, (2017) · Zbl 1381.81110
[2]	C. Vafa, Evidence for F-theory, Nucl. Phys.B 469 (1996) 403 [hep-th/9602022] [INSPIRE]. · Zbl 1003.81531
[3]	Martucci, L., Topological duality twist and brane instantons in F-theory, JHEP, 06, 180, (2014) · Zbl 1333.81349
[4]	B. Assel and S. Schäfer-Nameki, Six-dimensional origin of\( \mathcal{N}=4 \)SYM with duality defects, JHEP12 (2016) 058 [arXiv:1610.03663] [INSPIRE]. · Zbl 1390.81560
[5]	Haghighat, B.; Murthy, S.; Vafa, C.; Vandoren, S., F-theory, spinning black holes and multi-string branches, JHEP, 01, 009, (2016) · Zbl 1388.83817
[6]	C. Lawrie, S. Schäfer-Nameki and T. Weigand, Chiral 2D theories from N = 4 SYM with varying coupling, JHEP04 (2017) 111 [arXiv:1612.05640] [INSPIRE]. · Zbl 1378.81141
[7]	Ganor, OJ; Hong, YP; Tan, HS, Ground states of S-duality twisted N = 4 super Yang-Mills theory, JHEP, 03, 099, (2011) · Zbl 1301.81211
[8]	Benini, F.; Bobev, N., Two-dimensional SCFTs from wrapped branes and c-extremization, JHEP, 06, 005, (2013) · Zbl 1390.83325
[9]	Maldacena, JM; Strominger, A.; Witten, E., Black hole entropy in M-theory, JHEP, 12, 002, (1997) · Zbl 0951.83034
[10]	Lawrie, C.; Schäfer-Nameki, S.; Weigand, T., The gravitational sector of 2d (0, 2) F-theory vacua, JHEP, 05, 103, (2017) · Zbl 1380.83261
[11]	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
[12]	E. Silverstein and E. Witten, Global U(1)R symmetry and conformal invariance of (0, 2) models, Phys. Lett.B 328 (1994) 307 [hep-th/9403054] [INSPIRE]. · Zbl 1388.83817
[13]	Kim, N., Ads_{3} solutions of IIB supergravity from D3-branes, JHEP, 01, 094, (2006)
[14]	Donos, A.; Gauntlett, JP; Kim, N., AdS solutions through transgression, JHEP, 09, 021, (2008) · Zbl 1245.83060
[15]	Gauntlett, JP; Kim, N.; Waldram, D., Supersymmetric ads_{3}, ads_{2} and bubble solutions, JHEP, 04, 005, (2007)
[16]	Benini, F.; Bobev, N.; Crichigno, PM, Two-dimensional SCFTs from D3-branes, JHEP, 07, 020, (2016) · Zbl 1390.83088
[17]	J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Sasaki-Einstein metrics on S\^{}{2} × \(S\)\^{}{3}, Adv. Theor. Math. Phys.8 (2004) 711 [hep-th/0403002] [INSPIRE].
[18]	Benvenuti, S.; etal., An infinite family of superconformal quiver gauge theories with Sasaki-Einstein duals, JHEP, 06, 064, (2005)
[19]	F. Benini and S. Cremonesi, Partition functions of\( \mathcal{N}=\left(2,\ 2\right) \)gauge theories on S\^{}{2}and vortices, Commun. Math. Phys.334 (2015) 1483 [arXiv:1206.2356] [INSPIRE]. · Zbl 1308.81131
[20]	Doroud, N.; Gomis, J.; Floch, B.; Lee, S., Exact results in D = 2 supersymmetric gauge theories, JHEP, 05, 093, (2013) · Zbl 1342.81573
[21]	S. Datta, L. Eberhardt and M.R. Gaberdiel, Stringy\( \mathcal{N}=\left(2,\ 2\right) \)holography for AdS_{3}, JHEP01 (2018) 146 [arXiv:1709.06393] [INSPIRE].
[22]	L. Eberhardt, Supersymmetric AdS_{3}supergravity backgrounds and holography, JHEP02 (2018) 087 [arXiv:1710.09826] [INSPIRE]. · Zbl 1387.83102
[23]	A. Kehagias, New type IIB vacua and their F-theory interpretation, Phys. Lett.B 435 (1998) 337 [hep-th/9805131] [INSPIRE].
[24]	Aharony, O.; Fayyazuddin, A.; Maldacena, JM, The large N limit of N = 2, N = 1 field theories from three-branes in F-theory, JHEP, 07, 013, (1998) · Zbl 0958.81084
[25]	C.-h. Ahn, K. Oh and R. Tatar, The large N limit of N = 1 field theories from F-theory, Mod. Phys. Lett.A 14 (1999) 369 [hep-th/9808143] [INSPIRE].
[26]	A. Fayyazuddin and M. Spalinski, Large N superconformal gauge theories and supergravity orientifolds, Nucl. Phys.B 535 (1998) 219 [hep-th/9805096] [INSPIRE]. · Zbl 1080.81571
[27]	Kruczenski, M., Supergravity backgrounds corresponding to D7-branes wrapped on Kähler manifolds, JHEP, 01, 031, (2004) · Zbl 1243.83065
[28]	O. Aharony and Y. Tachikawa, A Holographic computation of the central charges of d = 4, N = 2 SCFTs, JHEP01 (2008) 037 [arXiv:0711.4532] [INSPIRE].
[29]	C. Couzens, D. Martelli, S. Schafer-Nameki and J. Sparks, F-theory and AdS_{5}/CFT_{4}, in progress.
[30]	Gauntlett, JP; Martelli, D.; Sparks, J.; Waldram, D., Supersymmetric ads_{5} solutions of type IIB supergravity, Class. Quant. Grav., 23, 4693, (2006) · Zbl 1096.83069
[31]	Gauntlett, JP; Pakis, S., The geometry of D = 11 Killing spinors, JHEP, 04, 039, (2003)
[32]	Kim, N.; Park, J-D, Comments on ads_{2} solutions of D = 11 supergravity, JHEP, 09, 041, (2006)
[33]	Gauntlett, JP; Martelli, D.; Sparks, J.; Waldram, D., Supersymmetric ads_{5} solutions of M-theory, Class. Quant. Grav., 21, 4335, (2004) · Zbl 1059.83038
[34]	J.P. Gauntlett, O.A.P. Mac Conamhna, T. Mateos and D. Waldram, New supersymmetric AdS_{3}solutions, Phys. Rev.D 74 (2006) 106007 [hep-th/0608055] [INSPIRE]. · Zbl 1228.83112
[35]	Brown, JD; Henneaux, M., Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys., 104, 207, (1986) · Zbl 0584.53039
[36]	Kraus, P.; Larsen, F., Holographic gravitational anomalies, JHEP, 01, 022, (2006)
[37]	M. Gabella, D. Martelli, A. Passias and J. Sparks, The free energy of\( \mathcal{N}=2 \)supersymmetric AdS_{4}solutions of M-theory, JHEP10 (2011) 039 [arXiv:1107.5035] [INSPIRE]. · Zbl 1303.81162
[38]	M. Gabella, D. Martelli, A. Passias and J. Sparks, \( \mathcal{N}=2 \)supersymmetric AdS_{4}solutions of M-theory, Commun. Math. Phys.325 (2014) 487 [arXiv:1207.3082] [INSPIRE]. · Zbl 1282.83010
[39]	Gauntlett, JP; Kim, N., Geometries with Killing spinors and supersymmetric AdS solutions, Commun. Math. Phys., 284, 897, (2008) · Zbl 1179.53078
[40]	Berenstein, D.; Herzog, CP; Klebanov, IR, Baryon spectra and AdS/CFT correspondence, JHEP, 06, 047, (2002)
[41]	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
[42]	D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Nonperturbative formulas for central functions of supersymmetric gauge theories, Nucl. Phys.B 526 (1998) 543 [hep-th/9708042] [INSPIRE]. · Zbl 1031.81565
[43]	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
[44]	Cassani, D.; Martelli, D., Supersymmetry on curved spaces and superconformal anomalies, JHEP, 10, 025, (2013) · Zbl 1342.81561
[45]	Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253, (1998) · Zbl 0914.53048
[46]	Martelli, D.; Sparks, J.; Yau, S-T, The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds, Commun. Math. Phys., 268, 39, (2006) · Zbl 1190.53041
[47]	C. Lawrie, D. Martelli and S. Schafer-Nameki, Anomaly polynomials for theories of class F, to appear. · Zbl 1402.83098
[48]	K.A. Intriligator, Bonus symmetries of N = 4 super-Yang-Mills correlation functions via AdS duality, Nucl. Phys.B 551 (1999) 575 [hep-th/9811047] [INSPIRE]. · Zbl 0947.81121
[49]	Franco, S.; etal., Gauge theories from toric geometry and brane tilings, JHEP, 01, 128, (2006)
[50]	Eager, R.; Schmude, J.; Tachikawa, Y., Superconformal indices, Sasaki-Einstein manifolds and cyclic homologies, Adv. Theor. Math. Phys., 18, 129, (2014) · Zbl 1309.81242
[51]	A. Amariti, L. Cassia and S. Penati, c-extremization from toric geometry, Nucl. Phys.B 929 (2018) 137 [arXiv:1706.07752] [INSPIRE]. · Zbl 1382.81146
[52]	Maldacena, JM; Núñez, C., Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys., A 16, 822, (2001) · Zbl 0984.83052
[53]	Butti, A.; Zaffaroni, A., R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization, JHEP, 11, 019, (2005) · Zbl 1090.81045
[54]	A. Dymarsky, I.R. Klebanov and N. Seiberg, On the moduli space of the cascading SU(\(M\) + \(p\)) × SU(\(P\)) gauge theory, JHEP01 (2006) 155 [hep-th/0511254] [INSPIRE]. · Zbl 0584.53039
[55]	Berenstein, D.; Herzog, CP; Ouyang, P.; Pinansky, S., Supersymmetry breaking from a Calabi-Yau singularity, JHEP, 09, 084, (2005)
[56]	Gauntlett, JP; Martelli, D.; Sparks, J.; Yau, S-T, Obstructions to the existence of Sasaki-Einstein metrics, Commun. Math. Phys., 273, 803, (2007) · Zbl 1149.53026
[57]	H.J. Kim, L.J. Romans and P. van Nieuwenhuizen, The mass spectrum of chiral N = 2 \(D\) = 10 supergravity on S\^{}{5}, Phys. Rev.D 32 (1985) 389 [INSPIRE].
[58]	M. Günaydin and N. Marcus, The spectrum of the S\^{}{5}compactification of the chiral N = 2, D = 10 supergravity and the unitary supermultiplets of U(2,2/4), Class. Quant. Grav.2 (1985) L11 [INSPIRE].
[59]	Shimizu, H.; Tachikawa, Y.; Zafrir, G., Anomaly matching on the Higgs branch, JHEP, 12, 127, (2017) · Zbl 1383.83190
[60]	K. Intriligator, 6d,\( \mathcal{N}=\left(1,\ 0\right) \)Coulomb branch anomaly matching, JHEP10 (2014) 162 [arXiv:1408.6745] [INSPIRE].
[61]	Witten, E., On flux quantization in M-theory and the effective action, J. Geom. Phys., 22, 1, (1997) · Zbl 0908.53065
[62]	A. Castro and W. Song, Comments on AdS_{2}gravity, arXiv:1411.1948 [INSPIRE].
[63]	D’Hoker, E.; Gutperle, M.; Karch, A.; Uhlemann, CF, Warped ads_{6} × S\^{}{2} in type IIB supergravity I: local solutions, JHEP, 08, 046, (2016) · Zbl 1390.83390
[64]	E. D’Hoker, M. Gutperle and C.F. Uhlemann, Warped AdS_{6} × \(S\)\^{}{2}in Type IIB supergravity II: global solutions and five-brane webs, JHEP05 (2017) 131 [arXiv:1703.08186] [INSPIRE]. · Zbl 1380.83282
[65]	E. D’Hoker, M. Gutperle and C.F. Uhlemann, Warped AdS_{6} × S\^{}{2}in Type IIB supergravity III: global solutions with seven-branes, JHEP11 (2017) 200 [arXiv:1706.00433] [INSPIRE]. · Zbl 1383.83202
[66]	I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys.B 536 (1998) 199 [hep-th/9807080] [INSPIRE]. · Zbl 0948.81619
[67]	D.R. Morrison and M.R. Plesser, Nonspherical horizons. 1., Adv. Theor. Math. Phys.3 (1999) 1 [hep-th/9810201] [INSPIRE].
[68]	Benini, F.; Canoura, F.; Cremonesi, S.; Núñez, C.; Ramallo, AV, Unquenched flavors in the Klebanov-Witten model, JHEP, 02, 090, (2007)
[69]	Klebanov, IR; Nekrasov, NA, Gravity duals of fractional branes and logarithmic RG flow, Nucl. Phys., B 574, 263, (2000) · Zbl 1056.81553
[70]	D. Martelli and J. Sparks, Symmetry-breaking vacua and baryon condensates in AdS/CFT, Phys. Rev.D 79 (2009) 065009 [arXiv:0804.3999] [INSPIRE].
[71]	N. Kim, The backreacted Kähler geometry of wrapped branes, Phys. Rev.D 86 (2012) 067901 [arXiv:1206.1536] [INSPIRE].
[72]	V. Apostolov, T. Draghici and A. Moroianu, A splitting theorem for Kähler manifolds whose Ricci tensors have constant eigenvalues, math/0007122. · Zbl 1111.53303
[73]	I. Bah, Quarter-BPS AdS_{5}solutions in M-theory with a T\^{}{2}bundle over a Riemann surface, JHEP08 (2013) 137 [arXiv:1304.4954] [INSPIRE]. · Zbl 1342.83321
[74]	B.R. Greene, A.D. Shapere, C. Vafa and S.-T. Yau, Stringy cosmic strings and noncompact Calabi-Yau manifolds, Nucl. Phys.B 337 (1990) 1 [INSPIRE]. · Zbl 0744.53045
[75]	C. Couzens, J. Gauntlett, D. Martelli and J. Sparks, The geometric dual of c-extremization, to appear. · Zbl 1245.83060
[76]	M. Cvetič, H. Lü, D.N. Page and C.N. Pope, New Einstein-Sasaki spaces in five and higher dimensions, Phys. Rev. Lett.95 (2005) 071101 [hep-th/0504225] [INSPIRE].
[77]	D. Martelli and J. Sparks, Toric Sasaki-Einstein metrics on S\^{}{2} × \(S\)\^{}{3}, Phys. Lett.B 621 (2005) 208 [hep-th/0505027] [INSPIRE].
[78]	A. Butti, D. Forcella and A. Zaffaroni, The dual superconformal theory for L\^{}{pqr}manifolds, JHEP09 (2005) 018 [hep-th/0505220] [INSPIRE]. · Zbl 1380.83261
[79]	Bertolini, M.; Bigazzi, F.; Cotrone, AL, New checks and subtleties for AdS/CFT and a-maximization, JHEP, 12, 024, (2004)
[80]	Herzog, CP; Ejaz, QJ; Klebanov, IR, Cascading RG flows from new Sasaki-Einstein manifolds, JHEP, 02, 009, (2005)