Abstract
We present and study ten-dimensional effective actions for various nongeometric fluxes of which exotic branes act as the magnetic sources. Each theory can be regarded as a U-dual version of the β-supergravity, a reformulation of the ten-dimensional supergravity which is suitable for describing non-geometric backgrounds with Q-flux. In each theory, we find a solution that corresponds to the background of an exotic brane and show that it is single-valued up to a gauge transformation, although the same background written in the standard background fields is not single-valued in a usual sense. Further, we also find a solution which corresponds to the background of an instanton that is the electric dual of the exotic brane and discuss its properties.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N.A. Obers and B. Pioline, U duality and M-theory, Phys. Rept. 318 (1999) 113 [hep-th/9809039] [INSPIRE].
E. Eyras and Y. Lozano, Exotic branes and nonperturbative seven-branes, Nucl. Phys. B 573 (2000) 735 [hep-th/9908094] [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].
E.A. Bergshoeff, T. Ortín and F. Riccioni, Defect branes, Nucl. Phys. B 856 (2012) 210 [arXiv:1109.4484] [INSPIRE].
J. de Boer and M. Shigemori, Exotic branes in string theory, Phys. Rept. 532 (2013) 65 [arXiv:1209.6056] [INSPIRE].
T. Kikuchi, T. Okada and Y. Sakatani, Rotating string in doubled geometry with generalized isometries, Phys. Rev. D 86 (2012) 046001 [arXiv:1205.5549] [INSPIRE].
F. Hassler and D. Lüst, Non-commutative/non-associative IIA (IIB) Q- and R-branes and their intersections, JHEP 07 (2013) 048 [arXiv:1303.1413] [INSPIRE].
D. Geissbuhler, D. Marques, C. Núñez and V. Penas, Exploring double field theory, JHEP 06 (2013) 101 [arXiv:1304.1472] [INSPIRE].
T. Kimura and S. Sasaki, Gauged linear σ-model for exotic five-brane, Nucl. Phys. B 876 (2013) 493 [arXiv:1304.4061] [INSPIRE].
T. Kimura and S. Sasaki, Worldsheet instanton corrections to 5 22 -brane geometry, JHEP 08 (2013) 126 [arXiv:1305.4439] [INSPIRE].
A. Chatzistavrakidis, F.F. Gautason, G. Moutsopoulos and M. Zagermann, Effective actions of nongeometric five-branes, Phys. Rev. D 89 (2014) 066004 [arXiv:1309.2653] [INSPIRE].
T. Kimura and S. Sasaki, Worldsheet description of exotic five-brane with two gauged isometries, JHEP 03 (2014) 128 [arXiv:1310.6163] [INSPIRE].
D. Andriot and A. Betz, NS-branes, source corrected Bianchi identities and more on backgrounds with non-geometric fluxes, JHEP 07 (2014) 059 [arXiv:1402.5972] [INSPIRE].
T. Kimura, S. Sasaki and M. Yata, World-volume effective actions of exotic five-branes, JHEP 07 (2014) 127 [arXiv:1404.5442] [INSPIRE].
T. Okada and Y. Sakatani, Defect branes as Alice strings, arXiv:1411.1043 [INSPIRE].
D. Andriot, M. Larfors, D. Lüst and P. Patalong, A ten-dimensional action for non-geometric fluxes, JHEP 09 (2011) 134 [arXiv:1106.4015] [INSPIRE].
D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, A geometric action for non-geometric fluxes, Phys. Rev. Lett. 108 (2012) 261602 [arXiv:1202.3060] [INSPIRE].
D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, Non-geometric fluxes in supergravity and double field theory, Fortsch. Phys. 60 (2012) 1150 [arXiv:1204.1979] [INSPIRE].
D. Andriot and A. Betz, β-supergravity: a ten-dimensional theory with non-geometric fluxes and its geometric framework, JHEP 12 (2013) 083 [arXiv:1306.4381] [INSPIRE].
D. Andriot and A. Betz, Supersymmetry with non-geometric fluxes, or a β-twist in generalized geometry and Dirac operator, arXiv:1411.6640 [INSPIRE].
G. Aldazabal, P.G. Camara, A. Font and L.E. Ibáñez, More dual fluxes and moduli fixing, JHEP 05 (2006) 070 [hep-th/0602089] [INSPIRE].
G. Aldazabal, P.G. Camara and J.A. Rosabal, Flux algebra, Bianchi identities and Freed-Witten anomalies in F-theory compactifications, Nucl. Phys. B 814 (2009) 21 [arXiv:0811.2900] [INSPIRE].
G. Aldazabal, E. Andres, P.G. Camara and M. Graña, U-dual fluxes and generalized geometry, JHEP 11 (2010) 083 [arXiv:1007.5509] [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, String solitons and T-duality, JHEP 05 (2011) 131 [arXiv:1102.0934] [INSPIRE].
E.A. Bergshoeff, J. Hartong, T. Ortín and D. Roest, Seven-branes and supersymmetry, JHEP 02 (2007) 003 [hep-th/0612072] [INSPIRE].
T. Kimura, Defect (p,q) five-branes, Nucl. Phys. B 893 (2015) 1 [arXiv:1410.8403] [INSPIRE].
C.M. Hull, Timelike T duality, de Sitter space, large-N gauge theories and topological field theory, JHEP 07 (1998) 021 [hep-th/9806146] [INSPIRE].
C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].
C. Hull and B. Zwiebach, Double field theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
C. Hull and B. Zwiebach, The gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [arXiv:0908.1792] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [INSPIRE].
O. Hohm, S.K. Kwak and B. Zwiebach, Double field theory of type II strings, JHEP 09 (2011) 013 [arXiv:1107.0008] [INSPIRE].
O. Hohm and S.K. Kwak, Frame-like geometry of double field theory, J. Phys. A 44 (2011) 085404 [arXiv:1011.4101] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Differential geometry with a projection: application to double field theory, JHEP 04 (2011) 014 [arXiv:1011.1324] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Stringy differential geometry, beyond Riemann, Phys. Rev. D 84 (2011) 044022 [arXiv:1105.6294] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Incorporation of fermions into double field theory, JHEP 11 (2011) 025 [arXiv:1109.2035] [INSPIRE].
O. Hohm and S.K. Kwak, N = 1 supersymmetric double field theory, JHEP 03 (2012) 080 [arXiv:1111.7293] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Supersymmetric double field theory: stringy reformulation of supergravity, Phys. Rev. D 85 (2012) 081501 [Erratum ibid. D 86 (2012) 089903] [arXiv:1112.0069] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Ramond-Ramond cohomology and O D,D T-duality, JHEP 09 (2012) 079 [arXiv:1206.3478] [INSPIRE].
O. Hohm and B. Zwiebach, Large gauge transformations in double field theory, JHEP 02 (2013) 075 [arXiv:1207.4198] [INSPIRE].
I. Jeon, K. Lee, J.-H. Park and Y. Suh, Stringy unification of type IIA and IIB supergravities under N = 2 D = 10 supersymmetric double field theory, Phys. Lett. B 723 (2013) 245 [arXiv:1210.5078] [INSPIRE].
D.S. Berman, C.D.A. Blair, E. Malek and M.J. Perry, The O D,D geometry of string theory, Int. J. Mod. Phys. A 29 (2014) 1450080 [arXiv:1303.6727] [INSPIRE].
B.R. Greene, A.D. Shapere, C. Vafa and S.-T. Yau, Stringy cosmic strings and noncompact Calabi-Yau manifolds, Nucl. Phys. B 337 (1990) 1 [INSPIRE].
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] [INSPIRE].
G.W. Gibbons, M.B. Green and M.J. Perry, Instantons and seven-branes in type IIB superstring theory, Phys. Lett. B 370 (1996) 37 [hep-th/9511080] [INSPIRE].
E. Bergshoeff, A. Collinucci, U. Gran, D. Roest and S. Vandoren, Non-extremal D-instantons, JHEP 10 (2004) 031 [hep-th/0406038] [INSPIRE].
E.A. Bergshoeff, J. Hartong, A. Ploegh and D. Sorokin, Q-instantons, JHEP 06 (2008) 028 [arXiv:0801.4956] [INSPIRE].
D.S. Berman and F.J. Rudolph, Branes are waves and monopoles, arXiv:1409.6314 [INSPIRE].
D.S. Berman and M.J. Perry, Generalized geometry and M-theory, JHEP 06 (2011) 074 [arXiv:1008.1763] [INSPIRE].
D.S. Berman, E.T. Musaev and M.J. Perry, Boundary terms in generalized geometry and doubled field theory, Phys. Lett. B 706 (2011) 228 [arXiv:1110.3097] [INSPIRE].
D.S. Berman, H. Godazgar, M. Godazgar and M.J. Perry, The local symmetries of M-theory and their formulation in generalised geometry, JHEP 01 (2012) 012 [arXiv:1110.3930] [INSPIRE].
D.S. Berman, H. Godazgar, M.J. Perry and P. West, Duality invariant actions and generalised geometry, JHEP 02 (2012) 108 [arXiv:1111.0459] [INSPIRE].
D.S. Berman, E.T. Musaev, D.C. Thompson and D.C. Thompson, Duality invariant M-theory: gauged supergravities and Scherk-Schwarz reductions, JHEP 10 (2012) 174 [arXiv:1208.0020] [INSPIRE].
D.S. Berman, M. Cederwall, A. Kleinschmidt and D.C. Thompson, The gauge structure of generalised diffeomorphisms, JHEP 01 (2013) 064 [arXiv:1208.5884] [INSPIRE].
J.-H. Park and Y. Suh, U-geometry: SL(5), JHEP 04 (2013) 147 [Erratum ibid. 11 (2013) 210] [arXiv:1302.1652] [INSPIRE].
O. Hohm and H. Samtleben, U-duality covariant gravity, JHEP 09 (2013) 080 [arXiv:1307.0509] [INSPIRE].
J.-H. Park and Y. Suh, U-gravity: SL(N), JHEP 06 (2014) 102 [arXiv:1402.5027] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional form of D = 11 supergravity, Phys. Rev. Lett. 111 (2013) 231601 [arXiv:1308.1673] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory I: E 6(6) covariant form of M-theory and type IIB, Phys. Rev. D 89 (2014) 066016 [arXiv:1312.0614] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory II: E 7(7), Phys. Rev. D 89 (2014) 066017 [arXiv:1312.4542] [INSPIRE].
H. Godazgar, M. Godazgar, O. Hohm, H. Nicolai and H. Samtleben, Supersymmetric E 7(7) exceptional field theory, JHEP 09 (2014) 044 [arXiv:1406.3235] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory III: E 8(8), Phys. Rev. D 90 (2014) 066002 [arXiv:1406.3348] [INSPIRE].
C.D.A. Blair and E. Malek, Geometry and fluxes of SL(5) exceptional field theory, arXiv:1412.0635 [INSPIRE].
D.S. Berman and F.J. Rudolph, Strings, branes and the self-dual solutions of exceptional field theory, arXiv:1412.2768 [INSPIRE].
E. Musaev and H. Samtleben, Fermions and supersymmetry in E 6(6) exceptional field theory, JHEP 03 (2015) 027 [arXiv:1412.7286] [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: 1412.8769
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
Sakatani, Y. Exotic branes and non-geometric fluxes. J. High Energ. Phys. 2015, 135 (2015). https://doi.org/10.1007/JHEP03(2015)135
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2015)135