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Evidence for F-theory. (English) Zbl 1003.81531
Summary: We construct compact examples of \(D\)-manifolds for type IIB strings. The construction has a natural interpretation in terms of compactification of a 12-dimensional F-theory. We provide evidence for a more natural reformulation of type IIB theory in terms of F-theory. Compactification of M-theory on a manifold \(K\) which admits elliptic fibration is equivalent to compactification of \(F\)-theory on \(K\times S^{1}\). A large class of \(N=1\) theories in 6 dimensions are obtained by compactification of F-theory on Calabi-Yau threefolds. A class of phenomenologically promising compactifications of \(F\)-theory is on Spin(7) holonomy manifolds down to 4 dimensions. This may provide a concrete realization of Witten’s proposal for solving the cosmological constant problem in four dimensions.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32J17 Compact complex \(3\)-folds
32J81 Applications of compact analytic spaces to the sciences
83E30 String and superstring theories in gravitational theory
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References:
[1] J. Schwarz, hep-th/9508143, hep-th/9510086.
[2] P. Horava and E. Witten, hep-th/9510209.
[3] K. Dasgupta and S. Mukhi, hep-th/9512196.
[4] E. Witten, hep-th/9512219.
[5] M.J. Duff, R. Minasian and E. Witten, hep-th/9601036.
[6] P.S. Aspinwall, hep-th/9508154.
[7] M. Bershadsky, V. Sadov and C. Vafa, hep-th/9510225.
[8] Ooguri, H.; Vafa, C.; Ooguri, H.; Ooguri, H., Mod. phys. lett. A, Nucl. phys. B, Nucl. phys. B, 367, 83, (1991)
[9] Witten, E., Int. J. mod. phys. A, 10, 1247, (1995), hep-th/9506101
[10] Hull, C.M.; Townsend, P.K., Nucl. phys. B, 438, 109, (1995)
[11] Greene, B.R.; Shapere, A.; Vafa, C.; Yau, S.-T., Nucl. phys. B, 337, 1, (1990)
[12] G. Gibbons, M.B. Green and M.J. Perry, hep-th/9511080.
[13] Dai, J.; Leigh, R.G.; Polchinski, J., Mod. phys. lett. A, 4, 2073, (1989)
[14] Horava, P, Phys. lett. B, 231, 251, (1989)
[15] M. Bershadsky, V. Sadov and C. Vafa, hep-th/9511222.
[16] M. Li, hep-th/9510161.
[17] Callan, C.G.; Lovelace, C.; Nappi, C.R.; Yost, S.A., Nucl. phys. B, 308, 221, (1988)
[18] M. Douglas, hep-th/9512077.
[19] C. Vafa and E. Witten, hep-th/9507050.
[20] E. Witten, hep-th/9503124.
[21] H. Ooguri and C. Vafa, hep-th/9511164.
[22] C. Vafa, unpublished.
[23] J. Polchinski and E. Witten, hep-th/9510169.
[24] J. Polchinski, hep-th/9510017.
[25] H. Ooguri and C. Vafa, hep-th/9505183.
[26] Siegel, W., Phys. rev. lett., 69, 1493, (1992)
[27] Bergshoeff, E.; Sezgin, E., Phys. lett. B, 292, 87, (1992)
[28] Blencowe, M.; Duff, M., Nucl. phys. B, 310, 387, (1988)
[29] P. Townsend et al., unpublished.
[30] C. Hull, hep-th/9512181.
[31] D. Morrison and C. Vafa, work in progress.
[32] Kachru, S.; Vafa, C., Nucl. phys. B, 450, 69, (1995)
[33] D Morrison, private communication.
[34] Schoen, C., J. math., 364, 85, (1986)
[35] Callan, C.G.; Harvey, J.A.; Strominger, A., Nucl. phys. B, 359, 611, (1991)
[36] A. Sen, hep-th/9602010.
[37] D.D. Joyce, Compact riemannian 7-manifolds with holonomy G2, to appear in J. Diff. Geom.; Compact riemannian 8-manifolds with holonomy spin(7), to appear in Inv. Math.
[38] Vafa, C.; Witten, E., Nucl. phys. B, 447, 261, (1995)
[39] C. Vafa and E. Witten, unpublished.
[40] E. Bergshoeff, B. Janssenhep and T. Ortin, hep-th/9506156; R. Khuri and T. Ortin, hep-th/9512178
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