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C. Córdova, D. S. Freed, H. T. Lam and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications II , SciPost Phys. 8
Original
1905
Earlier work this paper cites.
V. V. Nikulin, INTEGRAL SYMMETRIC BILINEAR FORMS AND SOME OF THEIR APPLICATIONS , Mathematics of the USSR-Izvestiya 14
1980
Earlier work this paper cites.
K. S. Narain, New Heterotic String Theories in Uncompactified Dimensions < < 10 , Phys. Lett. B 169
1986
Earlier work this paper cites.
K. S. Narain, M. H. Sarmadi and E. Witten, A Note on Toroidal Compactification of Heterotic String Theory , Nucl. Phys. B 279
1987
Earlier work this paper cites.
S. Chaudhuri, G. Hockney and J. D. Lykken, Maximally supersymmetric string theories in D < < 10 , Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
S. Chaudhuri and J. Polchinski, Moduli space of CHL strings , Phys. Rev. D 52
1995
Earlier work this paper cites.
C. Vafa, Evidence for F theory , Nucl. Phys. B 469
1996
Earlier work this paper cites.
A. Dabholkar and J. Park, Strings on orientifolds , Nucl. Phys. B 477
1996
Earlier work this paper cites.
P. S. Aspinwall and D. R. Morrison, Nonsimply connected gauge groups and rational points on elliptic curves , JHEP 07
1998
Earlier work this paper cites.
A. Mikhailov, Momentum lattice for CHL string , Nucl. Phys. B 534
1998
Earlier work this paper cites.
E. Witten, Toroidal compactification without vector structure , JHEP 02
1998
Earlier work this paper cites.

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Z. Guralnik, String junctions and nonsimply connected gauge groups , JHEP 07
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I. Shimada, On elliptic K3 surfaces , arXiv Mathematics e-prints (May, 2005) math/0505140, [ math/0505140 ]
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D. R. Morrison, S. Schafer-Nameki and B. Willett, Higher-Form Symmetries in 5d , JHEP 09
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F. Albertini, M. Del Zotto, I. García Etxebarria and S. S. Hosseini, Higher Form Symmetries and M-theory , JHEP 12
Original
2005
Cited alongside, same era.

Then

P. Benetti Genolini and L. Tizzano, Instantons, symmetries and anomalies in five dimensions , JHEP 04
Original
2009
Later among the works it cites.
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
Original
2014
Later among the works it cites.
Springer International Publishing, Cham, 2015
B. C. Hall, Lie Groups, Lie Algebras, and Representations · 2015
Later among the works it cites.
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries , JHEP 02
Original
2015
Later among the works it cites.
Y. Tachikawa, Frozen singularities in M and F theory , JHEP 06
Original
2016

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2021

On the Gauge Group Topology of 8d CHL Vacua

Cvetic, Mirjam, Dierigl, Markus, Lin, Ling et al.

Understand

Compactifications of the CHL string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice $\Lambda_M$, the so-called Mikhailov lattice.

Based on this data, we devise a method to determine the global gauge group structure including all $U(1)$ factors.
The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual.
Interpreting a non-trivial $\pi_1(G) \equiv {\cal Z}$ for the non-Abelian gauge group $G$ as having gauged a ${\cal Z}$ 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly (arXiv:2008.10605) that would obstruct this gauging.

Built on

C. Córdova, D. S. Freed, H. T. Lam and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications II , SciPost Phys. 8
Original
1905
Earlier work this paper cites.
V. V. Nikulin, INTEGRAL SYMMETRIC BILINEAR FORMS AND SOME OF THEIR APPLICATIONS , Mathematics of the USSR-Izvestiya 14
1980
Earlier work this paper cites.
K. S. Narain, New Heterotic String Theories in Uncompactified Dimensions < < 10 , Phys. Lett. B 169
1986
Earlier work this paper cites.
K. S. Narain, M. H. Sarmadi and E. Witten, A Note on Toroidal Compactification of Heterotic String Theory , Nucl. Phys. B 279
1987
Earlier work this paper cites.
S. Chaudhuri, G. Hockney and J. D. Lykken, Maximally supersymmetric string theories in D < < 10 , Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
S. Chaudhuri and J. Polchinski, Moduli space of CHL strings , Phys. Rev. D 52
1995
Earlier work this paper cites.
C. Vafa, Evidence for F theory , Nucl. Phys. B 469
1996
Earlier work this paper cites.
A. Dabholkar and J. Park, Strings on orientifolds , Nucl. Phys. B 477
1996
Earlier work this paper cites.
P. S. Aspinwall and D. R. Morrison, Nonsimply connected gauge groups and rational points on elliptic curves , JHEP 07
1998
Earlier work this paper cites.
A. Mikhailov, Momentum lattice for CHL string , Nucl. Phys. B 534
1998
Earlier work this paper cites.
E. Witten, Toroidal compactification without vector structure , JHEP 02
1998
Earlier work this paper cites.

Similar

Z. Guralnik, String junctions and nonsimply connected gauge groups , JHEP 07
2001
Cited alongside, same era.
Graduate Texts in Mathematics. Springer, 2004
D. Bump, Lie Groups · 2004
Cited alongside, same era.
I. Shimada, On elliptic K3 surfaces , arXiv Mathematics e-prints (May, 2005) math/0505140, [ math/0505140 ]
2005
Cited alongside, same era.
D. R. Morrison, S. Schafer-Nameki and B. Willett, Higher-Form Symmetries in 5d , JHEP 09
Original
2005
Cited alongside, same era.
F. Albertini, M. Del Zotto, I. García Etxebarria and S. S. Hosseini, Higher Form Symmetries and M-theory , JHEP 12
Original
2005
Cited alongside, same era.