Abstract
We analyze the anomaly constraints on 6D supergravity theories with a single abelian U(1) gauge factor. For theories with charges restricted to q = ±1, ±2 and no tensor multiplets, anomaly-free models match those models that can be realized from F-theory compactifications almost perfectly. For theories with tensor multiplets or with larger charges, the F-theory constraints are less well understood. We show, however, that there is an infinite class of distinct massless charge spectra in the “swampland” of theories that satisfy all known quantum consistency conditions but do not admit a realization through F-theory or any other known approach to string compactification. We also compare the spectra of charged matter in abelian theories with those that can be realized from breaking nonabelian SU(2) and higher rank gauge symmetries.
References
M.B. Green, J.H. Schwarz and P.C. West, Anomaly free chiral theories in six-dimensions, Nucl. Phys. B 254 (1985) 327 [INSPIRE].
A. Sagnotti, A note on the Green-Schwarz mechanism in open string theories, Phys. Lett. B 294 (1992) 196 [hep-th/9210127] [INSPIRE].
V. Kumar and W. Taylor, A bound on 6D N = 1 supergravities, JHEP 12 (2009) 050 [arXiv:0910.1586] [INSPIRE].
N. Seiberg and W. Taylor, Charge lattices and consistency of 6D supergravity, JHEP 06 (2011) 001 [arXiv:1103.0019] [INSPIRE].
V. Kumar and W. Taylor, String universality in six dimensions, Adv. Theor. Math. Phys. 15 (2011) 325 [arXiv:0906.0987] [INSPIRE].
C. Vafa, The string landscape and the swampland, hep-th/0509212 [INSPIRE].
H. Ooguri and C. Vafa, On the geometry of the string landscape and the swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].
V. Kumar, D.R. Morrison and W. Taylor, Global aspects of the space of 6D N = 1 supergravities, JHEP 11 (2010) 118 [arXiv:1008.1062] [INSPIRE].
S. Monnier, G.W. Moore and D.S. Park, Quantization of anomaly coefficients in 6D N = (1,0) supergravity, JHEP 02 (2018) 020 [arXiv:1711.04777] [INSPIRE].
J. Erler, Anomaly cancellation in six-dimensions, J. Math. Phys. 35 (1994) 1819 [hep-th/9304104] [INSPIRE].
V. Kumar, D.S. Park and W. Taylor, 6D supergravity without tensor multiplets, JHEP 04 (2011) 080 [arXiv:1011.0726] [INSPIRE].
D.S. Park and W. Taylor, Constraints on 6D supergravity theories with Abelian gauge symmetry, JHEP 01 (2012) 141 [arXiv:1110.5916] [INSPIRE].
V. Sadov, Generalized Green-Schwarz mechanism in F-theory, Phys. Lett. B 388 (1996) 45 [hep-th/9606008] [INSPIRE].
D.R. Morrison and D.S. Park, F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds, JHEP 10 (2012) 128 [arXiv:1208.2695] [INSPIRE].
D.S. Park, Anomaly equations and intersection theory, JHEP 01 (2012) 093 [arXiv:1111.2351] [INSPIRE].
E. Witten, An SU(2) anomaly, Phys. Lett. B 117 (1982) 324 [INSPIRE].
M. Bershadsky and C. Vafa, Global anomalies and geometric engineering of critical theories in six-dimensions, hep-th/9703167 [INSPIRE].
R. Suzuki and Y. Tachikawa, More anomaly-free models of six-dimensional gauged supergravity, J. Math. Phys. 47 (2006) 062302 [hep-th/0512019] [INSPIRE].
V. Kumar, D.R. Morrison and W. Taylor, Mapping 6D N = 1 supergravities to F-theory, JHEP 02 (2010) 099 [arXiv:0911.3393] [INSPIRE].
D.R. Morrison and W. Taylor, Matter and singularities, JHEP 01 (2012) 022 [arXiv:1106.3563] [INSPIRE].
L.B. Anderson, J. Gray, N. Raghuram and W. Taylor, Matter in transition, JHEP 04 (2016) 080 [arXiv:1512.05791] [INSPIRE].
D. Klevers, D.R. Morrison, N. Raghuram and W. Taylor, Exotic matter on singular divisors in F-theory, JHEP 11 (2017) 124 [arXiv:1706.08194] [INSPIRE].
A. Grassi and D.R. Morrison, Anomalies and the Euler characteristic of elliptic Calabi-Yau threefolds, Commun. Num. Theor. Phys. 6 (2012) 51 [arXiv:1109.0042] [INSPIRE].
N. Raghuram, Abelian F-theory models with charge-3 and charge-4 matter, JHEP 05 (2018) 050 [arXiv:1711.03210] [INSPIRE].
G. Martini and W. Taylor, 6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces, JHEP 06 (2015) 061 [arXiv:1404.6300] [INSPIRE].
D.R. Morrison, D.S. Park and W. Taylor, Non-Higgsable Abelian gauge symmetry and F-theory on fiber products of rational elliptic surfaces, arXiv:1610.06929 [INSPIRE].
D.R. Morrison and W. Taylor, Sections, multisections and U(1) fields in F-theory, arXiv:1404.1527 [INSPIRE].
M. Cvetič, D. Klevers, H. Piragua and W. Taylor, General U(1) × U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure, JHEP 11 (2015) 204 [arXiv:1507.05954] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 1, Nucl. Phys. B 473 (1996) 74 [hep-th/9602114] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 2, Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [INSPIRE].
D.R. Morrison and W. Taylor, Classifying bases for 6D F-theory models, Central Eur. J. Phys. 10 (2012) 1072 [arXiv:1201.1943] [INSPIRE].
C. Mayrhofer, D.R. Morrison, O. Till and T. Weigand, Mordell-Weil torsion and the global structure of gauge groups in F-theory, JHEP 10 (2014) 016 [arXiv:1405.3656] [INSPIRE].
D. Klevers, D.K. Mayorga Pena, P.-K. Oehlmann, H. Piragua and J. Reuter, F-theory on all toric hypersurface fibrations and its Higgs branches, JHEP 01 (2015) 142 [arXiv:1408.4808] [INSPIRE].
D. Klevers and W. Taylor, Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models, JHEP 06 (2016) 171 [arXiv:1604.01030] [INSPIRE].
V. Braun, T.W. Grimm and J. Keitel, Geometric engineering in toric F-theory and GUTs with U(1) gauge factors, JHEP 12 (2013) 069 [arXiv:1306.0577] [INSPIRE].
V. Braun, T.W. Grimm and J. Keitel, Complete intersection fibers in F-theory, JHEP 03 (2015) 125 [arXiv:1411.2615] [INSPIRE].
A. Collinucci, M. Fazzi, R. Valandro and D. Morrison, private communication, (2018).
A. Collinucci, M. Fazzi and R. Valandro, Geometric engineering on flops of length two, JHEP 04 (2018) 090 [arXiv:1802.00813] [INSPIRE].
T. Banks and N. Seiberg, Symmetries and strings in field theory and gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, to appear.
Y.-N. Wang, Tuned and non-Higgsable U(1)s in F-theory, JHEP 03 (2017) 140 [arXiv:1611.08665] [INSPIRE].
C. Lawrie, S. Schäfer-Nameki and J.-M. Wong, F-theory and all things rational: surveying U(1) symmetries with rational sections, JHEP 09 (2015) 144 [arXiv:1504.05593] [INSPIRE].
T.W. Grimm, A. Kapfer and D. Klevers, The arithmetic of elliptic fibrations in gauge theories on a circle, JHEP 06 (2016) 112 [arXiv:1510.04281] [INSPIRE].
M. Cvetič and L. Lin, The global gauge group structure of F-theory compactification with U(1)s, JHEP 01 (2018) 157 [arXiv:1706.08521] [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: 1803.04447
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
Taylor, W., Turner, A.P. An infinite swampland of U(1) charge spectra in 6D supergravity theories. J. High Energ. Phys. 2018, 10 (2018). https://doi.org/10.1007/JHEP06(2018)010
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2018)010
Keywords
- F-Theory
- Field Theories in Higher Dimensions
- Supergravity Models