Abstract
We use freely acting asymmetric orbifolds of type IIB string theory to construct a class of theories in five dimensions with eight supercharges whose moduli spaces for vector multiplets and hypermultiplets can be determined exactly. We argue that no quantum corrections to these moduli spaces arise. We focus on examples in which all moduli are in the NS-NS sector, while all fields from the R-R sector become massive. The full symmetry group of the moduli space is then determined by the subgroup of the T-duality group that survives the orbifold action. We illustrate this for freely acting orbifolds of type IIB string theory on T5 with 0, 1 or 2 hypermultiplets.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. Becker, M. Becker and A. Strominger, Five-branes, membranes and nonperturbative string theory, Nucl. Phys. B 456 (1995) 130 [hep-th/9507158] [INSPIRE].
A.C. Cadavid, A. Ceresole, R. D’Auria and S. Ferrara, Eleven-dimensional supergravity compactified on Calabi-Yau threefolds, Phys. Lett. B 357 (1995) 76 [hep-th/9506144] [INSPIRE].
E. Witten, Phase transitions in M theory and F theory, Nucl. Phys. B 471 (1996) 195 [hep-th/9603150] [INSPIRE].
I. Antoniadis, R. Minasian, S. Theisen and P. Vanhove, String loop corrections to the universal hypermultiplet, Class. Quant. Grav. 20 (2003) 5079 [hep-th/0307268] [INSPIRE].
D. Robles-Llana, F. Saueressig and S. Vandoren, String loop corrected hypermultiplet moduli spaces, JHEP 03 (2006) 081 [hep-th/0602164] [INSPIRE].
D. Robles-Llana et al., Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry, Phys. Rev. Lett. 98 (2007) 211602 [hep-th/0612027] [INSPIRE].
D. Robles-Llana, F. Saueressig, U. Theis and S. Vandoren, Membrane instantons from mirror symmetry, Commun. Num. Theor. Phys. 1 (2007) 681 [arXiv:0707.0838] [INSPIRE].
S. Alexandrov, B. Pioline, F. Saueressig and S. Vandoren, D-instantons and twistors, JHEP 03 (2009) 044 [arXiv:0812.4219] [INSPIRE].
S. Alexandrov, A. Sen and B. Stefański, D-instantons in Type IIA string theory on Calabi-Yau threefolds, JHEP 11 (2021) 018 [arXiv:2108.04265] [INSPIRE].
S. Alexandrov, A. Sen and B. Stefański, Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds, JHEP 12 (2021) 044 [arXiv:2110.06949] [INSPIRE].
S. Alexandrov and K. Bendriss, Hypermultiplet metric and NS5-instantons, JHEP 01 (2024) 140 [arXiv:2309.14440] [INSPIRE].
G. Gkountoumis, C. Hull, K. Stemerdink and S. Vandoren, Freely acting orbifolds of type IIB string theory on T5, JHEP 08 (2023) 089 [arXiv:2302.09112] [INSPIRE].
G. Papadopoulos and P.K. Townsend, Compactification of D = 11 supergravity on spaces of exceptional holonomy, Phys. Lett. B 357 (1995) 300 [hep-th/9506150] [INSPIRE].
I. Antoniadis, S. Ferrara and T.R. Taylor, N = 2 heterotic superstring and its dual theory in five-dimensions, Nucl. Phys. B 460 (1996) 489 [hep-th/9511108] [INSPIRE].
S. Ferrara, R.R. Khuri and R. Minasian, M theory on a Calabi-Yau manifold, Phys. Lett. B 375 (1996) 81 [hep-th/9602102] [INSPIRE].
F. Bonetti, T.W. Grimm and S. Hohenegger, Exploring 6D origins of 5D supergravities with Chern-Simons terms, JHEP 05 (2013) 124 [arXiv:1303.2661] [INSPIRE].
C. Vafa and E. Witten, Dual string pairs with N = 1 and N = 2 supersymmetry in four-dimensions, Nucl. Phys. B Proc. Suppl. 46 (1996) 225 [hep-th/9507050] [INSPIRE].
E. Kiritsis and C. Kounnas, Perturbative and nonperturbative partial supersymmetry breaking: N = 4 → N = 2 → N = 1, Nucl. Phys. B 503 (1997) 117 [hep-th/9703059] [INSPIRE].
A. Sen and C. Vafa, Dual pairs of type II string compactification, Nucl. Phys. B 455 (1995) 165 [hep-th/9508064] [INSPIRE].
A. Gregori et al., R**2 corrections and nonperturbative dualities of N = 4 string ground states, Nucl. Phys. B 510 (1998) 423 [hep-th/9708062] [INSPIRE].
Z.K. Baykara, Y. Hamada, H.-C. Tarazi and C. Vafa, On the string landscape without hypermultiplets, JHEP 04 (2024) 121 [arXiv:2309.15152] [INSPIRE].
C.M. Hull and P.K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
A. Gregori, C. Kounnas and J. Rizos, Classification of the N = 2, Z(2) x Z(2) symmetric type II orbifolds and their type II asymmetric duals, Nucl. Phys. B 549 (1999) 16 [hep-th/9901123] [INSPIRE].
A. Gregori, C. Kounnas and P.M. Petropoulos, Nonperturbative triality in heterotic and type II N = 2 strings, Nucl. Phys. B 553 (1999) 108 [hep-th/9901117] [INSPIRE].
K.S. Narain, M.H. Sarmadi and C. Vafa, Asymmetric Orbifolds, Nucl. Phys. B 288 (1987) 551 [INSPIRE].
K.S. Narain, M.H. Sarmadi and C. Vafa, Asymmetric orbifolds: Path integral and operator formulations, Nucl. Phys. B 356 (1991) 163 [INSPIRE].
K.S. Narain, New Heterotic String Theories in Uncompactified Dimensions < 10, Phys. Lett. B 169 (1986) 41 [INSPIRE].
W. Lerche, A.N. Schellekens and N.P. Warner, Lattices and Strings, Phys. Rept. 177 (1989) 1 [INSPIRE].
C. Vafa, Modular Invariance and Discrete Torsion on Orbifolds, Nucl. Phys. B 273 (1986) 592 [INSPIRE].
J.A. Harvey and G.W. Moore, An Uplifting Discussion of T-Duality, JHEP 05 (2018) 145 [arXiv:1707.08888] [INSPIRE].
A. Dabholkar and C. Hull, Duality twists, orbifolds, and fluxes, JHEP 09 (2003) 054 [hep-th/0210209] [INSPIRE].
M. Spalinski, Duality transformations in twisted Narain compactifications, Nucl. Phys. B 377 (1992) 339 [INSPIRE].
M. Spalinski, On the discrete symmetry group of Narian orbifolds, Phys. Lett. B 275 (1992) 47 [INSPIRE].
S. Ferrara, P. Fre and P. Soriani, On the moduli space of the T**6 / Z(3) orbifold and its modular group, Class. Quant. Grav. 9 (1992) 1649 [hep-th/9204040] [INSPIRE].
D. Bailin, A. Love, W.A. Sabra and S. Thomas, Modular symmetries in Z(N) orbifold compactified string theories with Wilson lines, Mod. Phys. Lett. A 9 (1994) 1229 [hep-th/9312122] [INSPIRE].
J. Erler and M. Spalinski, Modular groups for twisted Narain models, Int. J. Mod. Phys. A 9 (1994) 4407 [hep-th/9208038] [INSPIRE].
G. Lopes Cardoso, D. Lust and T. Mohaupt, Moduli spaces and target space duality symmetries in (0,2) Z(N) orbifold theories with continuous Wilson lines, Nucl. Phys. B 432 (1994) 68 [hep-th/9405002] [INSPIRE].
M.J. Duff and C.N. Pope, Consistent truncations in Kaluza-Klein theories, Nucl. Phys. B 255 (1985) 355 [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, Fortsch. Phys. 65 (2017) 1700048 [arXiv:1401.3360] [INSPIRE].
C. Hull, E. Marcus, K. Stemerdink and S. Vandoren, Black holes in string theory with duality twists, JHEP 07 (2020) 086 [arXiv:2003.11034] [INSPIRE].
M. Gunaydin, G. Sierra and P.K. Townsend, The Geometry of N = 2 Maxwell-Einstein Supergravity and Jordan Algebras, Nucl. Phys. B 242 (1984) 244 [INSPIRE].
M. Gunaydin, G. Sierra and P.K. Townsend, Exceptional Supergravity Theories and the MAGIC Square, Phys. Lett. B 133 (1983) 72 [INSPIRE].
B. de Wit and A. Van Proeyen, Special geometry, cubic polynomials and homogeneous quaternionic spaces, Commun. Math. Phys. 149 (1992) 307 [hep-th/9112027] [INSPIRE].
B. de Wit, F. Vanderseypen and A. Van Proeyen, Symmetry structure of special geometries, Nucl. Phys. B 400 (1993) 463 [hep-th/9210068] [INSPIRE].
M. Bianchi, G. Bossard and D. Consoli, Perturbative higher-derivative terms in \( \mathcal{N} \) = 6 asymmetric orbifolds, JHEP 06 (2022) 088 [arXiv:2203.15130] [INSPIRE].
M.J. Duff, Strong / weak coupling duality from the dual string, Nucl. Phys. B 442 (1995) 47 [hep-th/9501030] [INSPIRE].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
E. Palti, C. Vafa and T. Weigand, Supersymmetric Protection and the Swampland, JHEP 06 (2020) 168 [arXiv:2003.10452] [INSPIRE].
J.J. Heckman et al., On the Fate of Stringy Non-Invertible Symmetries, arXiv:2402.00118 [INSPIRE].
Acknowledgments
This work was initiated during a two-week visit at the Harvard Swampland Initiative. G.G. and S.V. are grateful for the warm hospitality, financial support and for stimulating discussions, in particular with Kaan Baykara and Cumrun Vafa. C.H. was supported by the STFC Consolidated Grants ST/T000791/1 and ST/X000575/1, and his research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2403.05650
Rights and permissions
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.
About this article
Cite this article
Gkountoumis, G., Hull, C. & Vandoren, S. Exact moduli spaces for \( \mathcal{N} \) = 2, D = 5 freely acting orbifolds. J. High Energ. Phys. 2024, 126 (2024). https://doi.org/10.1007/JHEP07(2024)126
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2024)126