×

zbMATH — the first resource for mathematics

Unity of superstring dualities. (English) Zbl 1052.83532
Summary: The effective action for type II string theory compactified on a six-torus is \(N=8\) supergravity, which is known to have an \(E_{7}\) duality symmetry. We show that this is broken by quantum effects to a discrete subgroup, \(E_{7}(\mathbb{Z})\), which contains both the \(T\)-duality group \(O(6, 6;\mathbb{Z})\) and the \(S\)-duality group SL\((2; \mathbb{Z})\). We present evidence for the conjecture that \(E_{7}(\mathbb{Z})\) is an exact ‘\(U\)-duality’ symmetry of type II string theory. This conjecture requires certain extreme black hole states to be identified with massive modes of the fundamental string. The gauge bosons from the Ramond-Ramond sector couple not to string excitations but to solitons. We discuss similar issues in the context of toroidal string compactifications to other dimensions, compactifications of the type II string on \(K_{3}\times T^{2}\) and compactifications of 11-dimensional supermembrane theory.

MSC:
83E30 String and superstring theories in gravitational theory
14E07 Birational automorphisms, Cremona group and generalizations
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Giveon, A.; Porrati, M.; Rabinovici, E., Phys. rep., 244, 77, (1994)
[2] Font, A.; Ibanez, L.; Lust, D.; Quevedo, F.; Rey, S.J., Phys. lett. B, Phys. rev. D, 43, 526, (1991)
[3] Schwarz, J.H.; Sen, A.; Schwarz, J.H.; Sen, A., Nucl. phys. B, Phys. lett. B, 312, 105, (1993)
[4] Sen, A.; Sen, A.; Sen, A.; Sen, A., Nucl. phys. B, Phys. lett. B, Int. J. mod. phys. A, Mod. phys. lett. A, 8, 2023, (1993)
[5] Narain, K.S., Phys. lett. B, 169, 41, (1986)
[6] Narain, K.S.; Sarmadi, M.H.; Witten, E., Nucl. phys. B, 279, 369, (1987)
[7] Cremmer, E.; Julia, B.; Cremmer, E.; Julia, B., Phys. lett. B, Nucl. phys. B, 159, 141, (1979)
[8] Gibbons, G.W.; Hull, C.M., Phys. lett. B, 109, 190, (1982)
[9] Gibbons, G.W., ()
[10] Kallosh, R.; Ortin, T., Phys. rev. D, 48, 742, (1993)
[11] Gibbons, G.W.; Perry, M.J., Nucl. phys. B, 248, 629, (1984)
[12] Hawking, S.W.; Salam, A.; Hooft, G.’t, (), Nucl. phys. B, 335, 138, (1990)
[13] Duff, M.J.; Khuri, R.R.; Minasian, R.; Rahmfeld, J., Nucl. phys. B, 418, 195, (1994)
[14] L. Susskind, preprint hep-th/9309145
[15] J.G. Russo and L. Susskind, preprint hep-th/9405117.
[16] M.J. Duff and J. Rahmfeld, preprint hep-th/9406105.
[17] Harvey, J.; Liu, J., Phys. lett. B, 268, 40, (1991)
[18] Gibbons, G.W.; Kastor, D.; London, L.; Townsend, P.K.; Traschen, J., Nucl. phys. B, 416, 850, (1994)
[19] Dabholkar, A.; Gibbons, G.W.; Harvey, J.A.; Ruiz-Ruiz, F.; Duff, M.J.; Gibbons, G.W.; Townsend, P.K., Nucl. phys. B, Phys. lett. B, 332, 321, (1991)
[20] Callan, C.; Harvey, J.; Strominger, A., Nucl. phys. B, 359, 611, (1991)
[21] Duff, M.J.; Lu, J.X.; Duff, M.J.; Lu, J.X., Nucl. phys. B, Phys. lett. B, 273, 409, (1991)
[22] Horowitz, G.T.; Strominger, A., Nucl. phys. B, 360, 197, (1991)
[23] Duff, M.J.; Lu, J.X., Nucl. phys. B, 416, 301, (1993)
[24] de Azcírraga, J.A.; Gauntlett, J.P.; Izquierdo, J.M.; Townsend, P.K., Phys. rev. lett., 63, 2443, (1989)
[25] Witten, E., Phys. lett. B, 153, 243, (1985)
[26] Townsend, P.K.; Green, M.B.; Schwarz, J.H.; West, P.C., Phys. lett. B, Nucl. phys. B, 254, 327, (1985)
[27] Bergshoeff, E.; Sezgin, E.; Townsend, P.K.; Bergshoeff, E.; Sezgin, E.; Townsend, P.K., Phys. lett. B, Ann. phys. (NY), 185, 330, (1988)
[28] Cremmer, E.; Julia, B.; Scherk, J., Phys. lett. B, 76, 409, (1978)
[29] Duff, M.J.; Nilsson, B.E.W.; Pope, C.N., Phys. lett. B, 129, 39, (1983)
[30] Duff, M.J.; Stelle, K.S., Phys. lett. B, 253, 113, (1991)
[31] Güven, R., Phys. lett. B, 276, 49, (1992)
[32] Gaillard, M.K.; Zumino, B., Nucl. phys. B, 193, 221, (1981)
[33] Günaydin, M.; Sierra, G.; Townsend, P.K.; Günaydin, M.; Sierra, G.; Townsend, P.K., Phys. lett. B, Nucl. phys. B, 242, 244, (1984)
[34] Witten, E., Phys. lett. B, 86, 283, (1979)
[35] Witten, E.; Olive, D., Phys. lett. B, 78, 97, (1978)
[36] Hull, C.M., Ph.D. thesis, (1983), Cambridge
[37] Gibbons, G.W.; Gibbons, G.W.; Maeda, K.; Garfinkle, D.; Horowitz, G.T.; Strominger, A.; Holzhey, C.F.; Wilczek, F.; Kallosh, R.; Linde, A.; Ortin, T.; Peet, A.; Van Proeyen, A., Nucl. phys. B, Nucl. phys. B, Phys. rev. D, Nucl. phys. B, Phys. rev. D, 46, 5278, (1992)
[38] Duff, M.J.; Khuri, R.R.; Minasian, R.; Rahmfeld, J., Nucl. phys. B, 418, 195, (1994)
[39] G.W. Gibbons, G.T. Horowitz and P.K. Townsend, Higher-dimensional resolution of dilatonic black hole singularities, Class. Quant. Grav., in press. · Zbl 0817.53054
[40] Gauntlett, J., Nucl. phys. B, 400, 103, (1993)
[41] Ruback, P., Commun. math. phys., 107, 93, (1986)
[42] Shiraishi, K., J. math. phys., 34, 4, 1480, (1993)
[43] Duff, M.J.; Lu, J.X., Nucl. phys. B, 390, 276, (1993)
[44] Felce, A.G.; Samols, T.M., Phys. lett. B, 308, 30, (1993)
[45] Bluhm; Goddard, P.; Dolan, L.; Bluhm; Goddard, P.; Dolan, L., Nucl. phys. B, Nucl. phys. B, 309, 330, (1988)
[46] Maharana, J.; Schwarz, J.H., Nucl. phys. B, 390, 3, (1993)
[47] de Roo, M., Nucl. phys. B, 255, 515, (1985)
[48] Gauntlett, J.; Harvey, J.; Liu, J., Nucl. phys. B, 409, 363, (1993)
[49] J. Gauntlett and J. Harvey, S-duality and the spectrum of magnetic monopoles in heterotic string theory, preprint EFI-94-36.
[50] Sorkin, R.; Gross, D.; Perry, M., Phys. rev. lett., Nucl. phys. B, 226, 29, (1983)
[51] Khuri, R.R., Phys. lett. B, 259, 261, (1991)
[52] Khuri, R.R., Nucl. phys. B, 387, 315, (1992)
[53] Banks, T.; Dine, M.; Dijkstra, H.; Fischler, W., Phys. lett. B, 212, 45, (1988)
[54] C.M. Hull, in preparation.
[55] Nepomechie, R., Phys. rev. D, 31, 1921, (1985)
[56] Strominger, A., Nucl. phys. B, 343, 167, (1990)
[57] Duff, M.J.; Lu, J.X., Phys. rev. lett., 66, 1402, (1991)
[58] Hull, C.M.; Alvarez-Gaumé, L.; Ginsparg, P., Nucl. phys. B, Commun. math. phys., 102, 311, (1985)
[59] G.T. Horowitz and A.A. Tseytlin, IC preprints Imperial /TP/93-94/38, Imperial /T9/93-94/54.
[60] Dai, J.; Leigh, R.G.; Polchinski, J.; Dine, M.; Huet, P.; Seiberg, N., Mod. phys. lett. A, Nucl. phys. B, 322, 301, (1989)
[61] Atiyah, M.; Hitchin, N.; Atiyah, M.; Hitchin, N.; Atiyah, M.; Hitchin, N., The geometry and dynamics of magnetic monopoles, Phys. lett. A, Philos. trans. R. soc. London A, 315, 459, (1988), Princeton U.P Princeton, NJ · Zbl 0671.53001
[62] Julia, B., ()
[63] Julia, B., (), 355
[64] Duff, M.J.; Lu, J.X., Nucl. phys. B, 347, 394, (1990)
[65] R.W. Gebert and H. Nicolai, preprint DESY-94-106 [hep-th 9406175].
[66] [65] A. Sen, Tata Institute preprint TIFR-TH-94-19 [hep-th 9408083].
[67] Cremmer, E., ()
[68] Teitelboim, C.; Teitelboim, C., Phys. lett. B, Phys. lett. B, 67, 69, (1986)
[69] Achúcarro, A.; Evans, J.; Townsend, P.K.; Wiltshire, D., Phys. lett. B, 198, 441, (1987)
[70] Hull, C.M., Phys. lett. B, 139, 39, (1984)
[71] Duff, M.J.; Gibbons, G.W.; Townsend, P.K., Phys. lett. B, 332, 321, (1994)
[72] Sen, A., Phys. lett. B, 329, 217, (1994)
[73] C. Vafa and E. Witten, Harvard preprint HUTP-94-A017 [hep-th/9408074.]
[74] Townsend, P.K., Phys. lett. B, 202, 53, (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.