Abstract
We study T-duality chains of five-branes in heterotic supergravity where the first order α′-corrections are present. By performing the α′-corrected T-duality transformations of the heterotic NS5-brane solutions, we obtain the KK5-brane and the exotic 5 22 -brane solutions associated with the symmetric, the neutral and the gauge NS5-branes. We find that the Yang-Mills gauge field in these solutions satisfies the self-duality condition in the three- and two-dimensional transverse spaces to the brane world-volumes. The O(2, 2) monodromy structures of the 5 22 -brane solutions are investigated by the α′-corrected generalized metric. Our analysis shows that the symmetric 5 22 -brane solution, which satisfies the standard embedding condition, is a T-fold and it exhibits the non-geometric nature. We also find that the neutral 5 22 -brane solution is a T-fold at least at \( \mathcal{O}\left({\alpha}^{\prime}\right) \). On the other hand, the gauge 5 22 -brane solution is not a T-fold but show unusual structures of space-time.
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].
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].
M. Blau and M. O’Loughlin, Aspects of U duality in matrix theory, Nucl. Phys. B 525 (1998) 182 [hep-th/9712047] [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].
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].
T. Kimura and S. Sasaki, Worldsheet description of exotic five-brane with two gauged isometries, JHEP 03 (2014) 128 [arXiv:1310.6163] [INSPIRE].
T. Kimura, Defect (p, q) five-branes, Nucl. Phys. B 893 (2015) 1 [arXiv:1410.8403] [INSPIRE].
T. Kimura, N = (4, 4) gauged linear σ-models for defect five-branes, arXiv:1503.08635 [INSPIRE].
T. Kimura, Gauge-fixing condition on prepotential of chiral multiplet for nongeometric backgrounds, Prog. Theor. Exp. Phys. 2016 (2016) 023B04 [arXiv:1506.05005] [INSPIRE].
T. Kimura, Semi-doubled σ-models for Five-branes, JHEP 02 (2016) 013 [arXiv:1512.05548] [INSPIRE].
T. Kimura, Supersymmetry projection rules on exotic branes, Prog. Theor. Exp. Phys. 2016 (2016) 053B05 [arXiv:1601.02175] [INSPIRE].
T. Kimura, Exotic brane junctions from F-theory, JHEP 05 (2016) 060 [arXiv:1602.08606] [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, Hyper-Kähler with torsion, T-duality and defect (p, q) five-branes, JHEP 03 (2015) 076 [arXiv:1411.3457] [INSPIRE].
E.A. Bergshoeff, T. Ortín and F. Riccioni, Defect branes, Nucl. Phys. B 856 (2012) 210 [arXiv:1109.4484] [INSPIRE].
M. Park and M. Shigemori, Codimension-2 solutions in five-dimensional supergravity, JHEP 10 (2015) 011 [arXiv:1505.05169] [INSPIRE].
T. Okada and Y. Sakatani, Defect branes as Alice strings, JHEP 03 (2015) 131 [arXiv:1411.1043] [INSPIRE].
C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [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].
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].
T.H. Buscher, A symmetry of the string background field equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].
T.H. Buscher, Path integral derivation of quantum duality in nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
A.A. Tseytlin, Duality and dilaton, Mod. Phys. Lett. A 6 (1991) 1721 [INSPIRE].
E. Bergshoeff, B. Janssen and T. Ortín, Solution generating transformations and the string effective action, Class. Quant. Grav. 13 (1996) 321 [hep-th/9506156] [INSPIRE].
M. Serone and M. Trapletti, A note on T-duality in heterotic string theory, Phys. Lett. B 637 (2006) 331 [hep-th/0512272] [INSPIRE].
A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167 [Erratum ibid. B 353 (1991) 565] [INSPIRE].
C.G. Callan Jr., J.A. Harvey and A. Strominger, World sheet approach to heterotic instantons and solitons, Nucl. Phys. B 359 (1991) 611 [INSPIRE].
C.G. Callan Jr., J.A. Harvey and A. Strominger, Worldbrane actions for string solitons, Nucl. Phys. B 367 (1991) 60 [INSPIRE].
M.J. Duff and J.X. Lu, Elementary five-brane solutions of D = 10 supergravity, Nucl. Phys. B 354 (1991) 141 [INSPIRE].
E. Bergshoeff and M. de Roo, Supersymmetric Chern-Simons terms in ten-dimensions, Phys. Lett. B 218 (1989) 210 [INSPIRE].
E.A. Bergshoeff and M. de Roo, The quartic effective action of the heterotic string and supersymmetry, Nucl. Phys. B 328 (1989) 439 [INSPIRE].
A.A. Belavin, A.M. Polyakov, A.S. Schwartz and Y.S. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, Phys. Lett. B 59 (1975) 85 [INSPIRE].
E. Witten, Small instantons in string theory, Nucl. Phys. B 460 (1996) 541 [hep-th/9511030] [INSPIRE].
R.R. Khuri, A heterotic multimonopole solution, Nucl. Phys. B 387 (1992) 315 [hep-th/9205081] [INSPIRE].
A.P. Protogenov, Exact classical solutions of Yang-Mills sourceless equations, Phys. Lett. B 67 (1977) 62 [INSPIRE].
J.P. Gauntlett, J.A. Harvey and J.T. Liu, Magnetic monopoles in string theory, Nucl. Phys. B 409 (1993) 363 [hep-th/9211056] [INSPIRE].
B.J. Harrington and H.K. Shepard, Periodic Euclidean solutions and the finite temperature Yang-Mills gas, Phys. Rev. D 17 (1978) 2122 [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].
M.J. Duff and R.R. Khuri, Four-dimensional string/string duality, Nucl. Phys. B 411 (1994) 473 [hep-th/9305142] [INSPIRE].
V.K. Onemli and B. Tekin, Kaluza-Klein vortices, JHEP 01 (2001) 034 [hep-th/0011287] [INSPIRE].
E. Bergshoeff, I. Entrop and R. Kallosh, Exact duality in string effective action, Phys. Rev. D 49 (1994) 6663 [hep-th/9401025] [INSPIRE].
K.S. Narain, New heterotic string theories in uncompactified dimensions < 10, Phys. Lett. B 169 (1986) 41 [INSPIRE].
K.S. Narain, M.H. Sarmadi and E. Witten, A note on toroidal compactification of heterotic string theory, Nucl. Phys. B 279 (1987) 369 [INSPIRE].
J. Maharana and J.H. Schwarz, Noncompact symmetries in string theory, Nucl. Phys. B 390 (1993) 3 [hep-th/9207016] [INSPIRE].
O. Hohm, A. Sen and B. Zwiebach, Heterotic effective action and duality symmetries revisited, JHEP 02 (2015) 079 [arXiv:1411.5696] [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].
D.S. Berman and F.J. Rudolph, Branes are waves and monopoles, JHEP 05 (2015) 015 [arXiv:1409.6314] [INSPIRE].
I. Bakhmatov, A. Kleinschmidt and E.T. Musaev, Non-geometric branes are DFT monopoles, JHEP 10 (2016) 076 [arXiv:1607.05450] [INSPIRE].
O. Hohm and S.K. Kwak, Double field theory formulation of heterotic strings, JHEP 06 (2011) 096 [arXiv:1103.2136] [INSPIRE].
K. Lee, Quadratic α ′ -corrections to heterotic double field theory, Nucl. Phys. B 899 (2015) 594 [arXiv:1504.00149] [INSPIRE].
O. Hohm, W. Siegel and B. Zwiebach, Doubled α ′ -geometry, JHEP 02 (2014) 065 [arXiv:1306.2970] [INSPIRE].
O. Hohm and B. Zwiebach, T-duality constraints on higher derivatives revisited, JHEP 04 (2016) 101 [arXiv:1510.00005] [INSPIRE].
O. Hohm and B. Zwiebach, Double metric, generalized metric and α ′ -deformed double field theory, Phys. Rev. D 93 (2016) 064035 [arXiv:1509.02930] [INSPIRE].
O. Hohm and B. Zwiebach, Double field theory at order α ′, JHEP 11 (2014) 075 [arXiv:1407.3803] [INSPIRE].
O. Hohm and B. Zwiebach, Green-Schwarz mechanism and α ′ -deformed Courant brackets, JHEP 01 (2015) 012 [arXiv:1407.0708] [INSPIRE].
O.A. Bedoya, D. Marques and C. Núñez, Heterotic α’-corrections in double field theory, JHEP 12 (2014) 074 [arXiv:1407.0365] [INSPIRE].
D. Marques and C.A. Núñez, T-duality and α ′ -corrections, JHEP 10 (2015) 084 [arXiv:1507.00652] [INSPIRE].
R. Blumenhagen and R. Sun, T-duality, non-geometry and Lie algebroids in heterotic double field theory, JHEP 02 (2015) 097 [arXiv:1411.3167] [INSPIRE].
A. Coimbra, R. Minasian, H. Triendl and D. Waldram, Generalised geometry for string corrections, JHEP 11 (2014) 160 [arXiv:1407.7542] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, Heterotic wrapping rules, JHEP 01 (2013) 005 [arXiv:1210.1422] [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].
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: 1608.01436
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
Sasaki, S., Yata, M. Non-geometric five-branes in heterotic supergravity. J. High Energ. Phys. 2016, 64 (2016). https://doi.org/10.1007/JHEP11(2016)064
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2016)064