Abstract
We derive a map relating the gauge symmetry groups of heterotic strings on T4 to other components of the moduli space with rank reduction. This generalizes the results for T2 and T3 which mirror the singularity freezing mechanism of K3 surfaces in F and M-theory, respectively. The novel feature in six dimensions is that the map explicitly involves the topology of the gauge groups, in particular acting only on non-simply-connected ones. This relation is equivalent to that of connected components of the moduli space of flat G-bundles over T2 with G non-simply-connected. These results are verified with a reasonably exhaustive list of gauge groups obtained with a moduli space exploration algorithm.
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References
J. de Boer et al., Triples, fluxes, and strings, Adv. Theor. Math. Phys. 4 (2002) 995 [hep-th/0103170] [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].
K. S. Narain, M. H. Sarmadi and C. Vafa, Asymmetric orbifolds, Nucl. Phys. B 288 (1987) 551 [INSPIRE].
S. Chaudhuri, G. Hockney and J. D. Lykken, Maximally supersymmetric string theories in D < 10, Phys. Rev. Lett. 75 (1995) 2264 [hep-th/9505054] [INSPIRE].
S. Chaudhuri and J. Polchinski, Moduli space of CHL strings, Phys. Rev. D 52 (1995) 7168 [hep-th/9506048] [INSPIRE].
W. Taylor, TASI lectures on supergravity and string vacua in various dimensions, arXiv:1104.2051 [INSPIRE].
A. Font, B. Fraiman, M. Graña, C. A. Núñez and H. P. De Freitas, Exploring the landscape of heterotic strings on T d , JHEP 10 (2020) 194 [arXiv:2007.10358] [INSPIRE].
A. Font, B. Fraiman, M. Graña, C. A. Núñez and H. Parra De Freitas, Exploring the landscape of CHL strings on Td , JHEP 08 (2021) 095 [arXiv:2104.07131] [INSPIRE].
A. Mikhailov, Momentum lattice for CHL string, Nucl. Phys. B 534 (1998) 612 [hep-th/9806030] [INSPIRE].
M. Cvetič, M. Dierigl, L. Lin and H. Y. Zhang, Gauge group topology of 8D Chaudhuri-Hockney-Lykken vacua, Phys. Rev. D 104 (2021) 086018 [arXiv:2107.04031] [INSPIRE].
F. A. Cachazo and C. Vafa, Type I’ and real algebraic geometry, hep-th/0001029 [INSPIRE].
B. Fraiman and H. P. De Freitas, Symmetry enhancements in 7d heterotic strings, JHEP 10 (2021) 002 [arXiv:2106.08189] [INSPIRE].
E. Witten, Toroidal compactification without vector structure, JHEP 02 (1998) 006 [hep-th/9712028] [INSPIRE].
L. Bhardwaj, D. R. Morrison, Y. Tachikawa and A. Tomasiello, The frozen phase of F-theory, JHEP 08 (2018) 138 [arXiv:1805.09070] [INSPIRE].
M. Atiyah and E. Witten, M theory dynamics on a manifold of G2 holonomy, Adv. Theor. Math. Phys. 6 (2003) 1 [hep-th/0107177] [INSPIRE].
Y. Tachikawa, Frozen singularities in M and F-theory, JHEP 06 (2016) 128 [arXiv:1508.06679] [INSPIRE].
C. Schweigert, On moduli spaces of flat connections with nonsimply connected structure group, Nucl. Phys. B 492 (1997) 743 [hep-th/9611092] [INSPIRE].
W. Lerche, C. Schweigert, R. Minasian and S. Theisen, A note on the geometry of CHL heterotic strings, Phys. Lett. B 424 (1998) 53 [hep-th/9711104] [INSPIRE].
P. S. Aspinwall and D. R. Morrison, Nonsimply connected gauge groups and rational points on elliptic curves, JHEP 07 (1998) 012 [hep-th/9805206] [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].
M. Cvetič and L. Lin, TASI Lectures on Abelian and Discrete Symmetries in F-theory, PoS TASI2017 (2018) 020 [arXiv:1809.00012] [INSPIRE].
B. Fraiman and H. Parra De Freitas, Symmetry enhancements in heterotic strings database, https://bernardofraiman.github.io/heterotic/ (2021).
B. Fraiman, M. Graña, and H. P. De Freitas, work-in-progress.
A. Bedroya, Y. Hamada, M. Montero and C. Vafa, Compactness of brane moduli and the String Lamppost Principle in d > 6, JHEP 02 (2022) 082 [arXiv:2110.10157] [INSPIRE].
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Fraiman, B., De Freitas, H.P. Freezing of gauge symmetries in the heterotic string on T4. J. High Energ. Phys. 2022, 7 (2022). https://doi.org/10.1007/JHEP04(2022)007
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DOI: https://doi.org/10.1007/JHEP04(2022)007