Abstract
We study stringy modifications of T3-fibered manifolds, where the fiber undergoes a monodromy in the T-duality group. We determine the fibration data defining such T-folds from a geometric model, by using a map between the duality group and the group of large diffeomorphisms of a four-torus. We describe the monodromies induced around duality defects where such fibrations degenerate and we argue that local solutions receive corrections from the winding sector, dual to the symmetry-breaking modes that correct semi-flat metrics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Strominger, S.-T. Yau and E. Zaslow, Mirror symmetry is T duality, Nucl. Phys. B 479 (1996) 243 [hep-th/9606040] [INSPIRE].
S. Hellerman, J. McGreevy and B. Williams, Geometric constructions of nongeometric string theories, JHEP 01 (2004) 024 [hep-th/0208174] [INSPIRE].
C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].
D. Vegh and J. McGreevy, Semi-flatland, JHEP 10 (2008) 068 [arXiv:0808.1569] [INSPIRE].
A. Kumar and C. Vafa, U manifolds, Phys. Lett. B 396 (1997) 85 [hep-th/9611007] [INSPIRE].
J.T. Liu and R. Minasian, U-branes and T 3 fibrations, Nucl. Phys. B 510 (1998) 538 [hep-th/9707125] [INSPIRE].
L. Martucci, J.F. Morales and D. Ricci Pacifici, Branes, U-folds and hyperelliptic fibrations, JHEP 01 (2013) 145 [arXiv:1207.6120] [INSPIRE].
J. de Boer and M. Shigemori, Exotic branes in string theory, Phys. Rept. 532 (2013) 65 [arXiv:1209.6056] [INSPIRE].
D. Lüst, S. Massai and V. Vall Camell, The monodromy of T-folds and T-fects, JHEP 09 (2016) 127 [arXiv:1508.01193] [INSPIRE].
C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
J. McOrist, D.R. Morrison and S. Sethi, Geometries, non-geometries and fluxes, Adv. Theor. Math. Phys. 14 (2010) 1515 [arXiv:1004.5447] [INSPIRE].
A. Malmendier and D.R. Morrison, K3 surfaces, modular forms and non-geometric heterotic compactifications, Lett. Math. Phys. 105 (2015) 1085 [arXiv:1406.4873] [INSPIRE].
I. García-Etxebarria, D. Lüst, S. Massai and C. Mayrhofer, Ubiquity of non-geometry in heterotic compactifications, JHEP 03 (2017) 046 [arXiv:1611.10291] [INSPIRE].
A. Font et al., Heterotic T-fects, 6D SCFTs and F-theory, JHEP 08 (2016) 175 [arXiv:1603.09361] [INSPIRE].
A. Font and C. Mayrhofer, Non-geometric vacua of the Spin(32)/ℤ2 heterotic string and little string theories, JHEP 11 (2017) 064 [arXiv:1708.05428] [INSPIRE].
A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept. 244 (1994) 77 [hep-th/9401139] [INSPIRE].
C. Bock, On low-dimensional solvmanifolds, arXiv:0903.2926.
R. Donagi, P. Gao and M.B. Schulz, Abelian fibrations, string junctions and flux/geometry duality, JHEP 04 (2009) 119 [arXiv:0810.5195] [INSPIRE].
M.B. Schulz, Calabi-Yau duals of torus orientifolds, JHEP 05 (2006) 023 [hep-th/0412270] [INSPIRE].
Y. Namikawa and K. Ueno, The complete classification of fibres in pencils of curves of genus two, Manuscripta Math. 9 (1973) 143.
A.B. Altman and S.L. Kleiman, The presentation functor and the compactified Jacobian, in The Grothendieck Festschrift , P. Cartier et al. eds., Birkhäuser Boston, Boston, U.S.A. (2007).
J. Kass, Notes on compactified Jacobian, lecture notes (2008).
R. Gompf and A. Stipsicz, 4-manifolds and Kirby Calculus, Graduate studies in mathematics. American Mathematical Society, U.S.A. (1999).
B. Farb and D. Margalit, A primer on mapping class groups, Princeton University Press, Princeton U.S.A. (2011).
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].
H. Ooguri and C. Vafa, Two-dimensional black hole and singularities of CY manifolds, Nucl. Phys. B 463 (1996) 55 [hep-th/9511164] [INSPIRE].
N.A. Obers and B. Pioline, U duality and M-theory, Phys. Rept. 318 (1999) 113 [hep-th/9809039] [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].
H. Ooguri and C. Vafa, Summing up D instantons, Phys. Rev. Lett. 77 (1996) 3296 [hep-th/9608079] [INSPIRE].
K. Becker and S. Sethi, Torsional heterotic geometries, Nucl. Phys. B 820 (2009) 1 [arXiv:0903.3769] [INSPIRE].
R. Gregory, J.A. Harvey and G.W. Moore, Unwinding strings and t duality of Kaluza-Klein and h monopoles, Adv. Theor. Math. Phys. 1 (1997) 283 [hep-th/9708086] [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, Worldsheet instanton corrections to 5 22 -brane geometry, JHEP 08 (2013) 126 [arXiv:1305.4439] [INSPIRE].
D. Lüst, E. Plauschinn and V. Vall Camell, Unwinding strings in semi-flatland, JHEP 07 (2017) 027 [arXiv:1706.00835] [INSPIRE].
A. Giveon and D. Kutasov, Little string theory in a double scaling limit, JHEP 10 (1999) 034 [hep-th/9909110] [INSPIRE].
D.R. Morrison, On the structure of supersymmetric T 3 fibrations, arXiv:1002.4921 [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: 1803.00550
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
Achmed-Zade, I., Hamilton, M.J.D., Lüst, D. et al. A note on T-folds and T3 fibrations. J. High Energ. Phys. 2018, 20 (2018). https://doi.org/10.1007/JHEP12(2018)020
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2018)020