Abstract
We construct the type-IIB AdS4 ⋉ K supergravity solutions which are dual to the three-dimensional \( \mathcal{N} = 4 \) superconformal field theories that arise as infrared fixed points of circular-quiver gauge theories. These superconformal field theories are labeled by a triple \( \left( {\rho, \hat{\rho},L} \right) \) subject to constraints, where ρ and \( \hat{\rho} \) are two partitions of a number N, and L is a positive integer. We show that in the limit of large L the localized five- branes in our solutions are effectively smeared, and these type-IIB solutions are dual to the near-horizon geometry of M-theory M2-branes at a \( {{{{{\mathbb{C}}^4}}} \left/ {{\left( {{Z_k}\times {Z_{\widehat{k}}}} \right)}} \right.} \) orbifold singularity. Our IIB solutions resolve the singularity into localized five-brane throats, without breaking the conformal symmetry. The constraints satisfied by the triple \( \left( {\rho, \hat{\rho},L} \right) \), together with the enhanced non-abelian flavour symmetries of the superconformal field theories are precisely reproduced by the type-IIB supergravity solutions. As a bonus, we uncover a novel type of “orbifold equivalence” between different quantum field theories and provide quantitative evidence for this equivalence.
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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] [INSPIRE].
S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
B. Assel, C. Bachas, J. Estes and J. Gomis, Holographic duals of D = 3 N = 4 superconformal field theories, JHEP 08 (2011) 087 [arXiv:1106.4253] [INSPIRE].
O. Aharony, L. Berdichevsky, M. Berkooz and I. Shamir, Near-horizon solutions for D3-branes ending on 5-branes, Phys. Rev. D 84 (2011) 126003 [arXiv:1106.1870] [INSPIRE].
J. Gomis and C. Romelsberger, Bubbling defect CFT’s, JHEP 08 (2006) 050[hep-th/0604155] [INSPIRE].
O. Lunin, On gravitational description of Wilson lines, JHEP 06 (2006) 026[hep-th/0604133] [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Exact half-BPS type IIB interface solutions. I. Local solution and supersymmetric Janus, JHEP 06 (2007) 021 [arXiv:0705.0022] [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Exact half-BPS type IIB interface solutions. II. Flux solutions and multi-Janus, JHEP 06 (2007) 022 [arXiv:0705.0024] [INSPIRE].
K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N = 4 superconformal Chern-Simons theories with hyper and twisted hyper multiplets, JHEP 07 (2008) 091 [arXiv:0805.3662] [INSPIRE].
M. Benna, I. Klebanov, T. Klose and M. Smedback, Supercnformal Chern-Simons theories and AdS4 /C F T3 correspondence, JHEP 09 (2008) 072 [arXiv:0806.1519] [INSPIRE].
Y. Imamura and S. Yokoyama, N = 4 Chern-Simons theories and wrapped M-branes in their gravity duals, Prog. Theor. Phys. 121 (2009) 915 [arXiv:0812.1331] [INSPIRE].
E. Witten, Branes, instantons, and Taub-NUT spaces, JHEP 06 (2009) 067 [arXiv:0902.0948] [INSPIRE].
O. Aharony, A. Hashimoto, S. Hirano, and P. Ouyang, D-brane charges in gravitational duals of 2 + 1 dimensional gauge theories and duality cascades, JHEP 01 (2010) 072[arXiv:0906.2390] [INSPIRE].
A. Dey, On three-dimensional mirror symmetry, JHEP 04 (2012) 051 [arXiv:1109.0407] [INSPIRE].
R. Gregory, J.A. Harvey, and G.W. Moore, Unwinding strings and t duality of Kaluza-Klein and h monopoles, Adv. Theor. Math. Phys. 1 (1997) 283, [hep-th/9708086] [INSPIRE].
D. Tong, N S5-branes, T duality and world sheet instantons, JHEP 07 (2002) 013[hep-th/0204186] [INSPIRE].
J. A. Harvey and S. Jensen, Worldsheet instanton corrections to the Kaluza-Klein monopole, JHEP 10 (2005) 028 [hep-th/0507204] [INSPIRE].
K. Okuyama, Linear sigma models of H and KK monopoles, JHEP 08 (2005) 089[hep-th/0508097] [INSPIRE].
C. Bachas, I. Brunner and D. Roggenkamp, A worldsheet extension of O(d, d : Z), JHEP 10 (2012) 039 [arXiv:1205.4647] [INSPIRE].
M.R. Douglas and G.W. Moore, D-branes, quivers and ALE instantons, hep-th/9603167 [INSPIRE].
D. Gaiotto and E. Witten, S-duality of boundary conditions in N = 4 super Yang-Mills theory, Adv. Theor. Math. Phys. 13 (2009) [arXiv:0807.3720] [INSPIRE].
J. de Boer, K. Hori, H. Ooguri, Y. Oz and Z. Yin, Mirror symmetry in three-dimensional theories, \( \mathrm{SL}\left( {2,\mathbb{Z}} \right) \) and D-brane moduli spaces, Nucl. Phys. B 493 (1997) 148 [hep-th/9612131] [INSPIRE].
P. Kronheimer, Instantons and the geometry of the nilpotent variety, J. Diff. Geom. 32 (1990) 473 [INSPIRE].
C. Bachas, J. Hoppe and B. Pioline, Nahm equations, N = 1∗ domain walls and D strings in AdS5 × S5 , JHEP 07 (2001) 041 [hep-th/0007067] [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
D.N. Page, Classical stability of round and squashed seven spheres in eleven-dimensional supergravity, Phys. Rev. D 28 (1983) 2976 [INSPIRE].
D. Marolf, Chern-Simons terms and the three notions of charge, hep-th/0006117 [INSPIRE].
C. Bachas and J. Estes, Spin-2 spectrum of defect theories, JHEP 06 (2011) 005 [arXiv:1103.2800] [INSPIRE].
M. B. Green, J. Schwarz, and E. Witten, Superstring theory. Volume 2: loop amplitudes, anomalies and phenomenology, Cambridge University Press, Cambridge U.K. (1988).
M. Morris, K. Thorne and U. Yurtsever, Wormholes, time machines and the weak energy condition, Phys. Rev. Lett. 61 (1988) 1446 [INSPIRE].
M. Morris and K. Thorne, Wormholes in space-time and their use for interstellar travel: A tool for teaching general relativity, Am. J. Phys. 56 (1988) 395.
M. Visser, Lorentzian wormholes: from Einstein to Hawking, American Institute of Physics, U.S.A. (1996).
T. Buscher, Path integral derivation of quantum duality in nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
H. Ooguri and C. Vafa, Two-dimensional black hole and singularities of CY manifolds, Nucl. Phys. B 463 (1996) 55 [hep-th/9511164] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M 2-branes and their gravity duals, JHEP 10 (2008) 091[arXiv:0806.1218] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M 2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
Y. Imamura and K. Kimura, On the moduli space of elliptic Maxwell-Chern-Simons theories, Prog. Theor. Phys. 120 (2008) 509 [arXiv:0806.3727] [INSPIRE].
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].
B. Assel, J. Estes and M. Yamazaki, Large-N free energy of 3D N = 4 SCFTs and AdS4 /C F T3 , JHEP 09 (2012) 074 [arXiv:1206.2920] [INSPIRE].
J.H. Schwarz and P.C. West, Symmetries and transformations of chiral N = 2 D = 10 supergravity, Phys. Lett. B 126 (1983) 301 [INSPIRE].
C. Hull and P. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
D. Gaiotto and E. Witten, Supersymmetric boundary conditions in N = 4 super Yang-Mills theory, J. Statist. Phys. 135 (2009) 789 [arXiv:0804.2902] [INSPIRE].
D. Gaiotto and E. Witten, Janus configurations, Chern-Simons couplings, and the θ-angle in N = 4 super Yang-Mills theory, JHEP 06 (2010) 097 [arXiv:0804.2907] [INSPIRE].
S. Kachru and E. Silverstein, 4D conformal theories and strings on orbifolds, Phys. Rev. Lett. 80 (1998) 4855 [hep-th/9802183] [INSPIRE].
A.E. Lawrence, N. Nekrasov and C. Vafa, On conformal field theories in four-dimensions, Nucl. Phys. B 533 (1998) 199 [hep-th/9803015] [INSPIRE].
M. Bershadsky, Z. Kakushadze and C. Vafa, String expansion as large-N expansion of gauge theories, Nucl. Phys. B 523 (1998) 59 [hep-th/9803076] [INSPIRE].
A. Armoni, M. Shifman and G. Veneziano, Refining the proof of planar equivalence, Phys. Rev. D 71 (2005) 045015 [hep-th/0412203] [INSPIRE].
P. Kovtun, M. Ünsal and L.G. Yaffe, Necessary and sufficient conditions for non-perturbative equivalences of large-Nc orbifold gauge theories, JHEP 07 (2005) 008 [hep-th/0411177] [INSPIRE].
M. Hanada, C. Hoyos and A. Karch, Generating new dualities through the orbifold equivalence: a demonstration in ABJM and four-dimensional quivers, JHEP 01 (2012) 068 [arXiv:1110.3803] [INSPIRE].
M. Hanada, C. Hoyos and H. Shimada, On a new type of orbifold equivalence and M-theoretic AdS4 /C F T3 duality, Phys. Lett. B 707 (2012) 394 [arXiv:1109.6127] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact results for Wilson loops in superconformal Chern-Simons theories with matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
Y. Imamura, Monopole operators in N = 4 Chern-Simons theories and wrapped M2-branes, Prog. Theor. Phys. 121 (2009) 1173 [arXiv:0902.4173] [INSPIRE].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
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Assel, B., Bachas, C., Estes, J. et al. IIB duals of D = 3 \( \mathcal{N} = 4 \) circular quivers. J. High Energ. Phys. 2012, 44 (2012). https://doi.org/10.1007/JHEP12(2012)044
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DOI: https://doi.org/10.1007/JHEP12(2012)044