Generic matter representations in 6D supergravity theories
- PDF / 2,860,409 Bytes
- 64 Pages / 595.276 x 841.89 pts (A4) Page_size
- 64 Downloads / 216 Views
Springer
Received: January 17, 2019 Accepted: May 4, 2019 Published: May 15, 2019
Washington Taylor and Andrew P. Turner Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, U.S.A.
E-mail: [email protected], [email protected] Abstract: In six-dimensional supergravity, there is a natural sense in which matter lying in certain representations of the gauge group is “generic,” in that other “exotic” matter representations require more fine tuning. From considerations of the dimensionality of the moduli space and anomaly cancellation conditions, we find that the generic sets of matter representations are well-defined for 6D supergravity theories with gauge groups containing arbitrary numbers of nonabelian factors and U(1) factors. These generic matter representations also match with those that arise in the most generic F-theory constructions, both in 6D and in 4D, with non-generic matter representations requiring more exotic singularity types. The analysis of generic versus exotic matter illuminates long-standing puzzles regarding F-theory models with multiple U(1) factors and provides a useful framework for analyzing the 6D “swampland” of apparently consistent low-energy theories that cannot be realized through known string constructions. We note also that the matter content of the standard model is generic by the criteria used here only if the global structure is SU(3)c × SU(2)L × U(1)Y /Z6 . Keywords: F-Theory, Field Theories in Higher Dimensions, Supergravity Models ArXiv ePrint: 1901.02012
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2019)081
JHEP05(2019)081
Generic matter representations in 6D supergravity theories
Contents 1 Introduction
1
2 Anomaly conditions in 6D supergravity
4 7 7 9 11 12 13 14 16 16 19 20 22 23 23 27 28
4 Generic matter in F-theory and the string swampland 4.1 Tate and Weierstrass models for SU(N ) gauge groups 4.2 U(1) matter in F-theory 4.2.1 One U(1) factor 4.2.2 Two U(1) factors 4.2.3 Three or more U(1) factors 4.3 Generic matter, string universality, and the swampland 4.3.1 Structure of 6D supergravity theories 4.3.2 Positivity cone and anomaly lattice related swampland issues 4.3.3 The swampland for generic matter 4.3.4 Exotic matter and the 6D swampland 4.3.5 Swampland summary
29 29 32 32 33 33 34 35 36 36 40 40
5 Generic matter with global gauge group structure and 4D physics 5.1 Generic matter and the global structure of the gauge group 5.2 Generic matter in 4D supergravity theories and F-theory models 5.3 Generic matter and the standard model
40 40 43 43
6 Conclusions
46
–i–
JHEP05(2019)081
3 Generic matter 3.1 Generic matter representations for G = SU(N1 ) × · · · × SU(Nr ) × U(1)s , s ≤ 3 3.2 Examples: generic U(1) and SU(2) matter 3.3 Anomaly constraints and generic matter content 3.4 Anomaly-equivalent exchanges and ambiguities in generic matter 3.5 Generic matter and anomaly coefficients 3.5.1 SU(2) generic matter and anomaly coefficients 3.5.2 U(1) generic matter and anomaly coefficients 3.5.3 M
Data Loading...
