Abstract
In recent years, it has been widely argued that the duality transformations of string and M-theory naturally imply the existence of so-called ‘exotic branes’ — low codimension objects with highly non-perturbative tensions, scaling as g αs for α ≤ −3. We argue that their intimate link with these duality transformations make them an ideal object of study using the general framework of Double Field Theory (DFT) and Exceptional Field Theory (EFT) — collectively referred to as ExFT. Parallel to the theme of dualities, we also stress that these theories unify known solutions in string- and M-theory into a single solution under ExFT. We argue that not only is there a natural unifying description of the lowest codimension objects, many of these exotic states require this formalism as a consistent supergravity description does not exist.
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].
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, T. Ortín and F. Riccioni, Defect Branes, Nucl. Phys. B 856 (2012) 210 [arXiv:1109.4484] [INSPIRE].
E.A. Bergshoeff, A. Marrani and F. Riccioni, Brane orbits, Nucl. Phys. B 861 (2012) 104 [arXiv:1201.5819] [INSPIRE].
E.A. Bergshoeff, A. Kleinschmidt and F. Riccioni, Supersymmetric Domain Walls, Phys. Rev. D 86 (2012) 085043 [arXiv:1206.5697] [INSPIRE].
S. Corley, A. Jevicki and S. Ramgoolam, Exact correlators of giant gravitons from dual N = 4 SYM theory, Adv. Theor. Math. Phys. 5 (2002) 809 [hep-th/0111222] [INSPIRE].
C.M. Hull, Doubled Geometry and T-Folds, JHEP 07 (2007) 080 [hep-th/0605149] [INSPIRE].
R.d. Sorkin, Kaluza-Klein Monopole, Phys. Rev. Lett. 51 (1983) 87 [INSPIRE].
D.J. Gross and M.J. Perry, Magnetic Monopoles in Kaluza-Klein Theories, Nucl. Phys. B 226 (1983) 29 [INSPIRE].
D.S. Berman and F.J. Rudolph, Strings, Branes and the Self-dual Solutions of Exceptional Field Theory, JHEP 05 (2015) 130 [arXiv:1412.2768] [INSPIRE].
J. Berkeley, D.S. Berman and F.J. Rudolph, Strings and Branes are Waves, JHEP 06 (2014) 006 [arXiv:1403.7198] [INSPIRE].
D.S. Berman and F.J. Rudolph, Branes are Waves and Monopoles, JHEP 05 (2015) 015 [arXiv:1409.6314] [INSPIRE].
Y. Sakatani, Exotic branes and non-geometric fluxes, JHEP 03 (2015) 135 [arXiv:1412.8769] [INSPIRE].
E.A. Bergshoeff, V.A. Penas, F. Riccioni and S. Risoli, Non-geometric fluxes and mixed-symmetry potentials, JHEP 11 (2015) 020 [arXiv:1508.00780] [INSPIRE].
I. Bakhmatov, A. Kleinschmidt and E.T. Musaev, Non-geometric branes are DFT monopoles, JHEP 10 (2016) 076 [arXiv:1607.05450] [INSPIRE].
E.A. Bergshoeff, O. Hohm, V.A. Penas and F. Riccioni, Dual Double Field Theory, JHEP 06 (2016) 026 [arXiv:1603.07380] [INSPIRE].
D.M. Lombardo, F. Riccioni and S. Risoli, P fluxes and exotic branes, JHEP 12 (2016) 114 [arXiv:1610.07975] [INSPIRE].
I. Bakhmatov, D. Berman, A. Kleinschmidt, E. Musaev and R. Otsuki, Exotic branes in Exceptional Field Theory: the SL(5) duality group, JHEP 08 (2018) 021 [arXiv:1710.09740] [INSPIRE].
P.C. West, E 11 and M-theory, Class. Quant. Grav. 18 (2001) 4443 [hep-th/0104081] [INSPIRE].
P.C. West, E 11 , SL(32) and central charges, Phys. Lett. B 575 (2003) 333 [hep-th/0307098] [INSPIRE].
P.C. West, E 11 origin of brane charges and U-duality multiplets, JHEP 08 (2004) 052 [hep-th/0406150] [INSPIRE].
P.C. West, Brane dynamics, central charges and E 11, JHEP 03 (2005) 077 [hep-th/0412336] [INSPIRE].
P.P. Cook and P.C. West, Charge multiplets and masses for E 11, JHEP 11 (2008) 091 [arXiv:0805.4451] [INSPIRE].
P.P. Cook, Exotic E 11 branes as composite gravitational solutions, Class. Quant. Grav. 26 (2009) 235023 [arXiv:0908.0485] [INSPIRE].
A.G. Tumanov and P. West, E 11 must be a symmetry of strings and branes, Phys. Lett. B 759 (2016) 663 [arXiv:1512.01644] [INSPIRE].
D.M. Lombardo, F. Riccioni and S. Risoli, Non-geometric fluxes & tadpole conditions for exotic branes, JHEP 10 (2017) 134 [arXiv:1704.08566] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, Wrapping rules (in) string theory, JHEP 01 (2018) 046 [arXiv:1710.00642] [INSPIRE].
A. Kleinschmidt, Counting supersymmetric branes, JHEP 10 (2011) 144 [arXiv:1109.2025] [INSPIRE].
T. Kimura and S. Sasaki, Worldsheet instanton corrections to 5 22 -brane geometry, JHEP 08 (2013) 126 [arXiv:1305.4439] [INSPIRE].
T. Kimura, S. Sasaki and K. Shiozawa, Worldsheet Instanton Corrections to Five-branes and Waves in Double Field Theory, JHEP 07 (2018) 001 [arXiv:1803.11087] [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, S. Sasaki and M. Yata, World-volume Effective Actions of Exotic Five-branes, JHEP 07 (2014) 127 [arXiv:1404.5442] [INSPIRE].
T. Kimura, S. Sasaki and M. Yata, World-volume Effective Action of Exotic Five-brane in M-theory, JHEP 02 (2016) 168 [arXiv:1601.05589] [INSPIRE].
K. Lee, S.-J. Rey and Y. Sakatani, Effective action for non-geometric fluxes duality covariant actions, JHEP 07 (2017) 075 [arXiv:1612.08738] [INSPIRE].
Y. Sakatani and S. Uehara, Connecting M-theory and type IIB parameterizations in Exceptional Field Theory, PTEP 2017 (2017) 043B05 [arXiv:1701.07819] [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].
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].
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].
C.M. Hull, Generalised Geometry for M-theory, JHEP 07 (2007) 079 [hep-th/0701203] [INSPIRE].
P. Pires Pacheco and D. Waldram, M-theory, exceptional generalised geometry and superpotentials, JHEP 09 (2008) 123 [arXiv:0804.1362] [INSPIRE].
C. Hillmann, Generalized E(7(7)) coset dynamics and D = 11 supergravity, JHEP 03 (2009) 135 [arXiv:0901.1581] [INSPIRE].
D.S. Berman and M.J. Perry, Generalized Geometry and M-theory, JHEP 06 (2011) 074 [arXiv:1008.1763] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as Generalised Geometry I: Type II Theories, JHEP 11 (2011) 091 [arXiv:1107.1733] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, E d(d) × ℝ+ generalised geometry, connections and M-theory, JHEP 02 (2014) 054 [arXiv:1112.3989] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as Generalised Geometry II: E d(d) × ℝ+ and M-theory, JHEP 03 (2014) 019 [arXiv:1212.1586] [INSPIRE].
G. Aldazabal, D. Marques and C. Núñez, Double Field Theory: A Pedagogical Review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].
D. Geissbuhler, D. Marques, C. Núñez and V. Penas, Exploring Double Field Theory, JHEP 06 (2013) 101 [arXiv:1304.1472] [INSPIRE].
D.S. Berman and D.C. Thompson, Duality Symmetric String and M-theory, Phys. Rept. 566 (2014) 1 [arXiv:1306.2643] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory. III. E 8(8), Phys. Rev. D 90 (2014) 066002 [arXiv:1406.3348] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory. II. E 7(7), Phys. Rev. D 89 (2014) 066017 [arXiv:1312.4542] [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].
A. Abzalov, I. Bakhmatov and E.T. Musaev, Exceptional field theory: SO(5, 5), JHEP 06 (2015) 088 [arXiv:1504.01523] [INSPIRE].
E.T. Musaev, Exceptional field theory: SL(5), JHEP 02 (2016) 012 [arXiv:1512.02163] [INSPIRE].
O. Hohm and Y.-N. Wang, Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory, JHEP 04 (2015) 050 [arXiv:1501.01600] [INSPIRE].
D.S. Berman, C.D.A. Blair, E. Malek and F.J. Rudolph, An action for F-theory: SL(2)ℝ+ exceptional field theory, Class. Quant. Grav. 33 (2016) 195009 [arXiv:1512.06115] [INSPIRE].
O. Hohm, D. Lüst and B. Zwiebach, The Spacetime of Double Field Theory: Review, Remarks and Outlook, Fortsch. Phys. 61 (2013) 926 [arXiv:1309.2977] [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].
E. Malek, U-duality in three and four dimensions, Int. J. Mod. Phys. A 32 (2017) 1750169 [arXiv:1205.6403] [INSPIRE].
C.D.A. Blair, E. Malek and J.-H. Park, M-theory and Type IIB from a Duality Manifest Action, JHEP 01 (2014) 172 [arXiv:1311.5109] [INSPIRE].
C.D.A. Blair and E. Malek, Geometry and fluxes of SL(5) exceptional field theory, JHEP 03 (2015) 144 [arXiv:1412.0635] [INSPIRE].
J.-H. Park and Y. Suh, U-geometry: SL(5), JHEP 04 (2013) 147 [Erratum ibid. 11 (2013) 210] [arXiv:1302.1652] [INSPIRE].
A. Le Diffon and H. Samtleben, Supergravities without an Action: Gauging the Trombone, Nucl. Phys. B 811 (2009) 1 [arXiv:0809.5180] [INSPIRE].
G. Aldazabal, M. Graña, D. Marqués and J.A. Rosabal, Extended geometry and gauged maximal supergravity, JHEP 06 (2013) 046 [arXiv:1302.5419] [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].
A. Le Diffon, H. Samtleben and M. Trigiante, N = 8 Supergravity with Local Scaling Symmetry, JHEP 04 (2011) 079 [arXiv:1103.2785] [INSPIRE].
C.D.A. Blair, Doubled strings, negative strings and null waves, JHEP 11 (2016) 042 [arXiv:1608.06818] [INSPIRE].
D. Tong, NS5-branes, T duality and world sheet instantons, JHEP 07 (2002) 013 [hep-th/0204186] [INSPIRE].
J.A. Harvey and S. Jensen, Worldsheet instanton corrections to the Kaluza-Klein monopole, JHEP 10 (2005) 028 [hep-th/0507204] [INSPIRE].
T. Kimura and S. Sasaki, Gauged Linear σ-model for Exotic Five-brane, Nucl. Phys. B 876 (2013) 493 [arXiv:1304.4061] [INSPIRE].
D. Lüst, E. Plauschinn and V. Vall Camell, Unwinding strings in semi-flatland, JHEP 07 (2017) 027 [arXiv:1706.00835] [INSPIRE].
E. Lozano-Tellechea and T. Ortín, 7-branes and higher Kaluza-Klein branes, Nucl. Phys. B 607 (2001) 213 [hep-th/0012051] [INSPIRE].
C.M. Hull, Gravitational duality, branes and charges, Nucl. Phys. Proc. Suppl. 62 (1998) 412 [INSPIRE].
E. Bergshoeff and J.P. van der Schaar, On M nine-branes, Class. Quant. Grav. 16 (1999) 23 [hep-th/9806069] [INSPIRE].
T. Ortin, Gravity and Strings, Cambridge Monographs on Mathematical Physics. Cambridge University Press (2015) [INSPIRE].
J.J. Fernández-Melgarejo, T. Kimura and Y. Sakatani, Weaving the Exotic Web, JHEP 09 (2018) 072 [arXiv:1805.12117] [INSPIRE].
A.G. Tumanov and P. West, E11 in 11D, Phys. Lett. B 758 (2016) 278 [arXiv:1601.03974] [INSPIRE].
A. Kleinschmidt and P.C. West, Representations of G+++ and the role of space-time, JHEP 02 (2004) 033 [hep-th/0312247] [INSPIRE].
P.P. Cook, Bound States of String Theory and Beyond, JHEP 03 (2012) 028 [arXiv:1109.6595] [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: 1806.00430
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Berman, D.S., Musaev, E.T. & Otsuki, R. Exotic branes in Exceptional Field Theory: E7(7) and beyond. J. High Energ. Phys. 2018, 53 (2018). https://doi.org/10.1007/JHEP12(2018)053
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2018)053