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\(SO(2,1)\) covariant IIB superalgebra. (English) Zbl 0958.81129

Summary: We propose a type IIB super-Poincaré algebra with \(SO(2,1)\) covariant central extension. Together with \(SO(2,1)\) and \(SO(9,1)\) generators, an \(SO(2,1)\) triplet (momenta), a Majorana-spinor doublet (supercharges) and a Rarita-Schwinger central charge generate a group, \(G\). We consider a coset \(G/H\) where \(H=(SO(2)\times \text{Lorentz})\), and the \(SL(2,\mathbb{R})\) 2-form doublet is obtained by the coset construction. It is shown that \(U(1)\) connections, whose strengths are associated with 2-forms, are recognized as coordinates of the enlarged space. We suggest that this is the fundamental algebra governing the superstring theories which explains the IIB \(SL(2,\mathbb{R})\) duality and geometrical origin of \(U(1)\) fields.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
17A70 Superalgebras
81R05 Finite-dimensional groups and algebras motivated by physics and their representations

References:

[1] Schwarz, J. H., Nucl. Phys. B, 226, 269 (1983)
[2] Schwarz, J. H., Phys. Lett. B, 364, 252 (1995), hep-th/9508143 (E)
[3] Vafa, C., Nucl. Phys. B, 469, 403 (1996), hep-th/9602022 · Zbl 1003.81531
[4] Bars, I., Phys. Rev. D, 56, 7954 (1997)
[5] Townsend, P. K., Phys. Lett. B, 373, 68 (1996), hep-th/9512062
[6] Aganagic, M.; Popescu, C.; Schwarz, J. H., Nucl. Phys. B, 496, 215 (1997) · Zbl 0935.83033
[7] Tseytlin, A. A., Nucl. Phys. B, 469, 51 (1996), hep-th/9602064 · Zbl 1002.81537
[8] Polchinski, J., Phys. Rev. Lett., 75, 4724 (1995) · Zbl 1020.81797
[9] TASI Lectures on D-branes, hep-th/9611050.; TASI Lectures on D-branes, hep-th/9611050.
[10] Hull, C. M., Nucl. Phys. B, 509, 216 (1998), hep-th/9705162 · Zbl 0934.83047
[11] De Azcarraga, J. A.; Izquierdo, J. M.; Townsend, P. K., Phys. Lett. B, 267, 366 (1991)
[12] M.R. Douglas, Branes within branes, hep-th/9512077.; M.R. Douglas, Branes within branes, hep-th/9512077. · Zbl 0946.81058
[13] Hatsuda, M.; Kamimura, K., Nucl. Phys. B, 520, 493 (1998), hep-th/9708001 · Zbl 0947.81061
[14] Hammer, H., Nucl. Phys. B, 521, 503 (1998), hep-th/9711009
[15] Kamimura, K.; Hatsuda, M., Nucl. Phys. B, 527, 381 (1998), hep-th/9712068 · Zbl 0951.81028
[16] Hatsuda, M.; Kamimura, K., Nucl. Phys. B, 535, 499 (1998), hep-th/9804087 · Zbl 1080.81576
[17] Igarashi, Y.; Itoh, K.; Kamimura, K., Nucl. Phys., B536, 469 (1998), hep-th/9806161
[18] Siegel, W., Phys. Rev. D, 50, 2799 (1994)
[19] Green, M., Phys. Lett. B, 223, 157 (1989)
[20] Sakaguchi, M., \((P, Q)\) strings and new space-time superalgebras (1999), hep-th/981143 · Zbl 0965.81084
[21] Sezgin, E., Phys. Lett. B, 392, 323 (1997), hep-th/9609086
[22] Cederwall, M.; Townsend, P. K., JHEP, 3, 9709 (1997), hep-th/9709002
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.