Abstract
We construct for arbitrary dimensions a universal T-duality covariant expression for the Wess-Zumino terms of supersymmetric String Solitons in toroidally compactified string theories with 32 supercharges. The worldvolume fields occurring in the effective action of these String Solitons form either a vector or a tensor multiplet with 16 supercharges. We determine the dimensions of the conjugacy classes under T-duality to which these String Solitons belong. We do this in two steps. First, we determine the T-duality representations of the p-forms of maximal supergravities that contain the potentials that couple to these String Solitons. We find that these are p-forms, with D − 4 ≤ p ≤ 6 if D ≥ 6 and with D − 4 ≤ p ≤ D if D < 6, transforming in the antisymmetric representation of rank m = p + 4 − D ≤ 4 of the T-duality symmetry SO(10 − D, 10 − D). All branes support vector multiplets except when m = 10 − D. In that case the T-duality representation splits, for D < 10, into a selfdual and anti-selfdual part, corresponding to 5-branes supporting either a vector or a tensor multiplet. In a second step we show that only certain well-defined lightlike directions in the anti-symmetric tensor representations of the T-duality group correspond to supersymmetric String Solitons. These lightlike directions define the conjugacy classes. As a by-product we show how by a straightforward procedure all solitonic fields of maximal supergravity are derived using the Kac-Moody algebra E11.
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References
E. Bergshoeff, M. de Roo, M.B. Green, G. Papadopoulos and P.K. Townsend, Duality of Type II 7-branes and 8-branes, Nucl. Phys. B 470 (1996) 113 [hep-th/9601150] [SPIRES].
E.A. Bergshoeff, M. de Roo, S.F. Kerstan and F. Riccioni, IIB Supergravity Revisited, JHEP 08 (2005) 098 [hep-th/0506013] [SPIRES].
E.A. Bergshoeff, M. de Roo, S.F. Kerstan, T. Ortín and F. Riccioni, IIA ten-forms and the gauge algebras of maximal supergravity theories, JHEP 07 (2006) 018 [hep-th/0602280] [SPIRES].
E.A. Bergshoeff, J. Hartong, P.S. Howe, T. Ortín and F. Riccioni, IIA/ IIB Supergravity and Ten-forms, JHEP 05 (2010) 061 [arXiv:1004.1348] [SPIRES].
L.J. Romans, Massive N = 2a Supergravity in Ten-Dimensions, Phys. Lett. B 169 (1986) 374 [SPIRES].
B. de Wit, H. Nicolai and H. Samtleben, Gauged Supergravities, Tensor Hierarchies and M-theory, JHEP 02 (2008) 044 [arXiv:0801.1294] [SPIRES].
F. Riccioni and P.C. West, The E 11 origin of all maximal supergravities, JHEP 07 (2007) 063 [arXiv:0705.0752] [SPIRES].
E.A. Bergshoeff, I. De Baetselier and T.A. Nutma, E 11 and the embedding tensor, JHEP 09 (2007) 047 [arXiv:0705.1304] [SPIRES].
P.C. West, E 11 and M-theory, Class. Quant. Grav. 18 (2001) 4443 [hep-th/0104081] [SPIRES].
E.A. Bergshoeff and F. Riccioni, D-Brane Wess-Zumino Terms and U-duality, JHEP 11 (2010) 139 [arXiv:1009.4657] [SPIRES].
P.P. Cook and P.C. West, Charge multiplets and masses for E 11, JHEP 11 (2008) 091 [arXiv:0805.4451] [SPIRES].
P.P. Cook, Exotic E 11 branes as composite gravitational solutions, Class. Quant. Grav. 26 (2009) 235023 [arXiv:0908.0485] [SPIRES].
J.H. Schwarz, An SL(2, Z) multiplet of type IIB superstrings, Phys. Lett. B 360 (1995) 13 [hep-th/9508143] [SPIRES].
M. Aganagic, J. Park, C. Popescu and J.H. Schwarz, Dual D-brane actions, Nucl. Phys. B 496 (1997) 215 [hep-th/9702133] [SPIRES].
P.K. Townsend, Membrane tension and manifest IIB S-duality, Phys. Lett. B 409 (1997) 131 [hep-th/9705160] [SPIRES].
M. Cederwall and A. Westerberg, World-volume fields, SL(2, Z) and duality: The type IIB 3-brane, JHEP 02 (1998) 004 [hep-th/9710007] [SPIRES].
A. Westerberg and N. Wyllard, Towards a manifestly SL(2, Z)-covariant action for the type IIB (p,q) super-five-branes, JHEP 06 (1999) 006 [hep-th/9905019] [SPIRES].
E.A. Bergshoeff, M. de Roo, S.F. Kerstan, T. Ortín and F. Riccioni, SL(2,R)-invariant IIB brane actions, JHEP 02 (2007) 007 [hep-th/0611036] [SPIRES].
C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [SPIRES].
C.M. Hull, Doubled geometry and T-folds, JHEP 07 (2007) 080 [hep-th/0605149] [SPIRES].
C.M. Hull and R.A. Reid-Edwards, Gauge Symmetry, T-duality and Doubled Geometry, JHEP 08 (2008) 043 [arXiv:0711.4818] [SPIRES].
P. Meessen and T. Ortín, An SL(2, Z) multiplet of nine-dimensional type-II supergravity theories, Nucl. Phys. B 541 (1999) 195 [hep-th/9806120] [SPIRES].
G. Dall’Agata, K. Lechner and M. Tonin, D = 10, N = IIB supergravity: Lorentz-invariant actions and duality, JHEP 07 (1998) 017 [hep-th/9806140] [SPIRES].
E.A. Bergshoeff, J. Hartong, T. Ortín and D. Roest, Seven-branes and supersymmetry, JHEP 02 (2007) 003 [hep-th/0612072] [SPIRES].
E.A. Bergshoeff, M. de Roo, S.F. Kerstan, T. Ortín and F. Riccioni, IIB nine-branes, JHEP 06 (2006) 006 [hep-th/0601128] [SPIRES].
R. Slansky, Group Theory for Unified Model Building, Phys. Rept. 79 (1981) 1 [SPIRES].
P.K. Townsend, M-theory from its superalgebra, hep-th/9712004 [SPIRES].
E. Bergshoeff, B. Janssen and T. Ortín, Kaluza-Klein monopoles and gauged σ-models, Phys. Lett. B 410 (1997) 131 [hep-th/9706117] [SPIRES].
I. Schnakenburg and P.C. West, Kac-Moody symmetries of IIB supergravity, Phys. Lett. B 517 (2001) 421 [hep-th/0107181] [SPIRES].
A. Kleinschmidt, I. Schnakenburg and P.C. West, Very-extended Kac-Moody algebras and their interpretation at low levels, Class. Quant. Grav. 21 (2004) 2493 [hep-th/0309198] [SPIRES].
M.R. Gaberdiel, D.I. Olive and P.C. West, A class of Lorentzian Kac-Moody algebras, Nucl. Phys. B 645 (2002) 403 [hep-th/0205068] [SPIRES].
T. Damour, M. Henneaux and H. Nicolai, E 10 and a ’small tension expansion’ of M-theory, Phys. Rev. Lett. 89 (2002) 221601 [hep-th/0207267] [SPIRES].
P.C. West, Very extended E 8 and A 8 at low levels, gravity and supergravity, Class. Quant. Grav. 20 (2003) 2393 [hep-th/0212291] [SPIRES].
F. Riccioni and P.C. West, Dual fields and E 11, Phys. Lett. B 645 (2007) 286 [hep-th/0612001] [SPIRES].
V.G. Kac, Infinite dimensional Lie algebras, Cambridge Univ. Pr., Cambridge U.K. (1990) [SPIRES].
P.C. West, The IIA, IIB and eleven dimensional theories and their common E 11 origin, Nucl. Phys. B 693 (2004) 76 [hep-th/0402140] [SPIRES].
E.A. Bergshoeff, M. de Roo, S.F. Kerstan, A. Kleinschmidt and F. Riccioni, Dual Gravity and Matter, Gen. Rel. Grav. 41 (2009) 39 [arXiv:0803.1963] [SPIRES].
A. Van Proeyen, Tools for supersymmetry, hep-th/9910030 [SPIRES].
F. Riccioni, Low-energy structure of six-dimensional open-string vacua, hep-th/0203157 [SPIRES].
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ArXiv ePrint: 1102.0934
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Bergshoeff, E.A., Riccioni, F. String solitons and T-duality. J. High Energ. Phys. 2011, 131 (2011). https://doi.org/10.1007/JHEP05(2011)131
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DOI: https://doi.org/10.1007/JHEP05(2011)131