Abstract
In this paper we show that the number of all 1/2-BPS branes in string theory compactified on a torus can be derived by universal wrapping rules whose formulation we present. These rules even apply to branes in less than ten dimensions whose ten-dimensional origin is an exotic brane. In that case the wrapping rules contain an additional combinatorial factor that is related to the highest dimension in which the ten-dimensional exotic brane, after compactification, can be realized as a standard brane. We show that the wrapping rules also apply to cases with less supersymmetry. As a specific example, we discuss the compactification of IIA/IIB string theory on (T4/ℤ2) × Tn.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C.M. Hull and P.K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
J. Polchinski, String theory. Volume 1: An introduction to the bosonic string, Cambridge University Press, Cambridge U.K. (1998).
J. Polchinski, String theory. Volume 2: Superstring theory and beyond, Cambridge University Press, Cambridge U.K. (1998).
K. Becker, M. Becker and J.H. Schwarz, String theory and M-theory: A modern introduction, Cambridge University Press, Cambridge U.K. (2007).
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] [INSPIRE].
P.C. West, E 11 and M-theory, Class. Quant. Grav. 18 (2001) 4443 [hep-th/0104081] [INSPIRE].
E.A. Bergshoeff, M. de Roo, S.F. Kerstan and F. Riccioni, IIB supergravity revisited, JHEP 08 (2005) 098 [hep-th/0506013] [INSPIRE].
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] [INSPIRE].
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] [INSPIRE].
F. Riccioni and P.C. West, The E 11 origin of all maximal supergravities, JHEP 07 (2007) 063 [arXiv:0705.0752] [INSPIRE].
E.A. Bergshoeff, I. De Baetselier and T.A. Nutma, E 11 and the embedding tensor, JHEP 09 (2007) 047 [arXiv:0705.1304] [INSPIRE].
B. de Wit, H. Nicolai and H. Samtleben, Gauged Supergravities, Tensor Hierarchies and M-theory, JHEP 02 (2008) 044 [arXiv:0801.1294] [INSPIRE].
H. Nicolai and H. Samtleben, Maximal gauged supergravity in three-dimensions, Phys. Rev. Lett. 86 (2001) 1686 [hep-th/0010076] [INSPIRE].
B. de Wit, H. Samtleben and M. Trigiante, On Lagrangians and gaugings of maximal supergravities, Nucl. Phys. B 655 (2003) 93 [hep-th/0212239] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, D-Brane Wess-Zumino Terms and U-duality, JHEP 11 (2010) 139 [arXiv:1009.4657] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, The D-brane U-scan, Proc. Symp. Pure Math. 85 (2012) 313 [arXiv:1109.1725] [INSPIRE].
E.A. Bergshoeff, A. Marrani and F. Riccioni, Brane orbits, Nucl. Phys. B 861 (2012) 104 [arXiv:1201.5819] [INSPIRE].
E.A. Bergshoeff, F. Riccioni and L. Romano, Branes, Weights and Central Charges, JHEP 06 (2013) 019 [arXiv:1303.0221] [INSPIRE].
A. Kleinschmidt, Counting supersymmetric branes, JHEP 10 (2011) 144 [arXiv:1109.2025] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, String Solitons and T-duality, JHEP 05 (2011) 131 [arXiv:1102.0934] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, Branes and wrapping rules, Phys. Lett. B 704 (2011) 367 [arXiv:1108.5067] [INSPIRE].
E.A. Bergshoeff, T. Ortín and F. Riccioni, Defect Branes, Nucl. Phys. B 856 (2012) 210 [arXiv:1109.4484] [INSPIRE].
S. Elitzur, A. Giveon, D. Kutasov and E. Rabinovici, Algebraic aspects of matrix theory on T d, Nucl. Phys. B 509 (1998) 122 [hep-th/9707217] [INSPIRE].
N.A. Obers and B. Pioline, U-duality and M-theory, Phys. Rept. 318 (1999) 113 [hep-th/9809039] [INSPIRE].
E. Lozano-Tellechea and T. Ortín, 7-branes and higher Kaluza-Klein branes, Nucl. Phys. B 607 (2001) 213 [hep-th/0012051] [INSPIRE].
J. de Boer and M. Shigemori, Exotic branes and non-geometric backgrounds, Phys. Rev. Lett. 104 (2010) 251603 [arXiv:1004.2521] [INSPIRE].
J. de Boer and M. Shigemori, Exotic Branes in String Theory, Phys. Rept. 532 (2013) 65 [arXiv:1209.6056] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, Dual doubled geometry, Phys. Lett. B 702 (2011) 281 [arXiv:1106.0212] [INSPIRE].
D.M. Lombardo, F. Riccioni and S. Risoli, P fluxes and exotic branes, JHEP 12 (2016) 114 [arXiv:1610.07975] [INSPIRE].
G. Pradisi and F. Riccioni, Non-geometric orbifolds and wrapping rules, JHEP 09 (2014) 170 [arXiv:1407.5576] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, Heterotic wrapping rules, JHEP 01 (2013) 005 [arXiv:1210.1422] [INSPIRE].
E.A. Bergshoeff, C. Condeescu, G. Pradisi and F. Riccioni, Heterotic-Type II duality and wrapping rules, JHEP 12 (2013) 057 [arXiv:1311.3578] [INSPIRE].
E.A. Bergshoeff, F. Riccioni and L. Romano, Towards a classification of branes in theories with eight supercharges, JHEP 05 (2014) 070 [arXiv:1402.2557] [INSPIRE].
W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].
C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].
E.A. Bergshoeff, O. Hohm, V.A. Penas and F. Riccioni, Dual Double Field Theory, JHEP 06 (2016) 026 [arXiv:1603.07380] [INSPIRE].
C.M. Hull, Strongly coupled gravity and duality, Nucl. Phys. B 583 (2000) 237 [hep-th/0004195] [INSPIRE].
X. Bekaert, N. Boulanger and M. Henneaux, Consistent deformations of dual formulations of linearized gravity: A No go result, Phys. Rev. D 67 (2003) 044010 [hep-th/0210278] [INSPIRE].
X. Bekaert, N. Boulanger and S. Cnockaert, No self-interaction for two-column massless fields, J. Math. Phys. 46 (2005) 012303 [hep-th/0407102] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1710.00642
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Bergshoeff, E.A., Riccioni, F. Wrapping rules (in) string theory. J. High Energ. Phys. 2018, 46 (2018). https://doi.org/10.1007/JHEP01(2018)046
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2018)046