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A stringy origin of M2 brane Chern-Simons theories. (English) Zbl 1204.81131

Summary: We show that string duality relates M-theory on a local Calabi-Yau fourfold singularity \(X_{4}\) to type IIA string theory on a Calabi-Yau threefold \(X_{3}\) fibered over a real line, with RR 2-form fluxes turned on. The RR flux encodes how the M-theory circle is fibered over the IIA geometry. The theories on \(N\) D2 branes probing \(X_{3}\) are the well-known quiver theories with \({\mathcal N}=2\) supersymmetry in three dimensions. We show that turning on fluxes, and fibering the \(X_{3}\) over a direction transverse to the branes, corresponds to turning on \({\mathcal N}=2\) Chern-Simons couplings. String duality implies that, in the strong coupling limit, the \(N\) D2 branes on \(X_{3}\) in this background become \(N\) M2 branes on \(X_{4}\). This provides a string theory derivation for the recently conjectured description of the M2 brane theories on Calabi-Yau fourfolds in terms of \({\mathcal N}=2\) quiver Chern-Simons theories. We also provide a new \({\mathcal N}=2\) Chern-Simons theory dual to \(AdS_{4}\times Q^{1,1,1}\). Type IIA/M-theory duality also relates IIA string theory on \(X_{3}\) with only the RR fluxes turned on, to M-theory on a \(G_{2}\) holonomy manifold. We show that this implies that the \(N\) M2 branes probing the \(G_{2}\) manifold are described by the quiver Chern-Simons theory originating from the D2 branes probing \(X_{3}\), except that now Chern-Simons terms preserve only \({\mathcal N}=1\) supersymmetry in three dimensions.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T60 Supersymmetric field theories in quantum mechanics

References:

[1] Duff, M. J.; Nilsson, B. E.W.; Pope, C. N., Kaluza-Klein supergravity, Phys. Rep., 130, 1 (1986) · Zbl 0588.53073
[2] Schwarz, J. H., Superconformal Chern-Simons theories, JHEP, 0411, 078 (2004)
[3] Aharony, O.; Bergman, O.; Jafferis, D. L.; Maldacena, J., \(N = 6\) superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP, 0810, 091 (2008) · Zbl 1245.81130
[4] Martelli, D.; Sparks, J., Moduli spaces of Chern-Simons quiver gauge theories and AdS(4)/CFT(3), Phys. Rev. D, 78, 126005 (2008)
[5] Hanany, A.; Zaffaroni, A., Tilings, Chern-Simons theories and M2 branes, JHEP, 0810, 111 (2008) · Zbl 1245.81176
[6] Jafferis, D. L.; Tomasiello, A., A simple class of \(N = 3\) gauge/gravity duals, JHEP, 0810, 101 (2008) · Zbl 1245.83066
[7] Hanany, A.; Vegh, D.; Zaffaroni, A., Brane tilings and M2 branes, JHEP, 0903, 012 (2009)
[8] Ueda, K.; Yamazaki, M., Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories, JHEP, 0812, 045 (2008) · Zbl 1329.81326
[9] Franco, S.; Hanany, A.; Park, J.; Rodriguez-Gomez, D., Towards M2-brane theories for generic toric singularities, JHEP, 0812, 110 (2008) · Zbl 1329.81312
[10] Davey, J.; Hanany, A.; Mekareeya, N.; Torri, G., Phases of M2-brane theories
[11] Hanany, A.; He, Y. H., M2-branes and quiver Chern-Simons: A taxonomic study
[12] Cachazo, F.; Fiol, B.; Intriligator, K. A.; Katz, S.; Vafa, C., A geometric unification of dualities, Nucl. Phys. B, 628, 3 (2002) · Zbl 0992.83072
[13] Franco, S.; Hanany, A.; Kennaway, K. D.; Vegh, D.; Wecht, B., Brane dimers and quiver gauge theories, JHEP, 0601, 096 (2006)
[14] Franco, S.; Hanany, A.; Martelli, D.; Sparks, J.; Vegh, D.; Wecht, B., Gauge theories from toric geometry and brane tilings, JHEP, 0601, 128 (2006)
[15] Feng, B.; He, Y. H.; Kennaway, K. D.; Vafa, C., Dimer models from mirror symmetry and quivering amoebae, Adv. Theor. Math. Phys., 12, 3 (2008) · Zbl 1144.81501
[16] Denef, F., Quantum quivers and Hall/hole halos, JHEP, 0210, 023 (2002)
[17] Ooguri, H.; Yamazaki, M., Crystal melting and toric Calabi-Yau manifolds · Zbl 1179.81139
[18] Hori, K.; Iqbal, A.; Vafa, C., D-branes and mirror symmetry
[19] Feng, B.; Hanany, A.; He, Y. H., Phase structure of D-brane gauge theories and toric duality, JHEP, 0108, 040 (2001) · Zbl 0972.81138
[20] Franco, S.; Klebanov, I. R.; Rodriguez-Gomez, D., M2-branes on orbifolds of the cone over \(Q^{1, 1, 1}\)
[21] Acharya, B. S.; Figueroa-O’Farrill, J. M.; Hull, C. M.; Spence, B. J., Branes at conical singularities and holography, Adv. Theor. Math. Phys., 2, 1249 (1999) · Zbl 0948.83061
[22] Martelli, D.; Sparks, J., Notes on toric Sasaki-Einstein seven-manifolds and \(AdS_4 / CFT_3\), JHEP, 0811, 016 (2008)
[23] Aganagic, M.; Vafa, C., G(2) manifolds, mirror symmetry and geometric engineering
[24] Douglas, M. R.; Moore, G. W., D-branes, quivers, and ALE instantons
[25] Amariti, A.; Forcella, D.; Girardello, L.; Mariotti, A., 3D Seiberg-like Dualities and M2 Branes · Zbl 1288.81084
[26] Witten, E., Phases of \(N = 2\) theories in two dimensions, Nucl. Phys. B, 403, 159 (1993) · Zbl 0910.14020
[27] Denef, F., Les houches lectures on constructing string vacua
[28] Kachru, S.; Simic, D., Stringy instantons in IIB brane systems
[29] Diaconescu, D. E.; Douglas, M. R.; Gomis, J., Fractional branes and wrapped branes, JHEP, 9802, 013 (1998) · Zbl 1060.81576
[30] Gaiotto, D.; Tomasiello, A., The gauge dual of Romans mass · Zbl 1269.81126
[31] Gaiotto, D.; Tomasiello, A., Perturbing gauge/gravity duals by a Romans mass · Zbl 1181.83204
[32] Douglas, M. R.; Greene, B. R.; Morrison, D. R., Orbifold resolution by D-branes, Nucl. Phys. B, 506, 84 (1997) · Zbl 0925.81266
[33] Atiyah, M.; Maldacena, J. M.; Vafa, C., An M-theory flop as a large N duality, J. Math. Phys., 42, 3209 (2001) · Zbl 1061.81056
[34] Atiyah, M.; Witten, E., M-theory dynamics on a manifold of G(2) holonomy, Adv. Theor. Math. Phys., 6, 1 (2003)
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