Niemeier Lattices in the Free Fermionic Heterotic–String Formulation
The spinor–vector duality was discovered in free fermionic constructions of the heterotic string in four dimensions. It played a key role in the construction of heterotic–string models with an anomaly-free extra Z′ symmetry that may remain unbroken down to low energy scales. A generic signature of t...
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/3572469 |
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| author | Panos Athanasopoulos Alon E. Faraggi |
| author_facet | Panos Athanasopoulos Alon E. Faraggi |
| author_sort | Panos Athanasopoulos |
| collection | DOAJ |
| description | The spinor–vector duality was discovered in free fermionic constructions of the heterotic string in four dimensions. It played a key role in the construction of heterotic–string models with an anomaly-free extra Z′ symmetry that may remain unbroken down to low energy scales. A generic signature of the low scale string derived Z′ model is via diphoton excess that may be within reach of the LHC. A fascinating possibility is that the spinor–vector duality symmetry is rooted in the structure of the heterotic–string compactifications to two dimensions. The two-dimensional heterotic–string theories are in turn related to the so-called moonshine symmetries that underlie the two-dimensional compactifications. In this paper, we embark on exploration of this connection by the free fermionic formulation to classify the symmetries of the two-dimensional heterotic–string theories. We use two complementary approaches in our classification. The first utilises a construction which is akin to the one used in the spinor–vector duality. Underlying this method is the triality property of SO(8) representations. In the second approach, we use the free fermionic tools to classify the twenty-four-dimensional Niemeier lattices. |
| format | Article |
| id | doaj-art-47f1c48f7f6c4419a65ebada5bcf54f9 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-47f1c48f7f6c4419a65ebada5bcf54f92025-02-03T05:47:25ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/35724693572469Niemeier Lattices in the Free Fermionic Heterotic–String FormulationPanos Athanasopoulos0Alon E. Faraggi1Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UKDepartment of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UKThe spinor–vector duality was discovered in free fermionic constructions of the heterotic string in four dimensions. It played a key role in the construction of heterotic–string models with an anomaly-free extra Z′ symmetry that may remain unbroken down to low energy scales. A generic signature of the low scale string derived Z′ model is via diphoton excess that may be within reach of the LHC. A fascinating possibility is that the spinor–vector duality symmetry is rooted in the structure of the heterotic–string compactifications to two dimensions. The two-dimensional heterotic–string theories are in turn related to the so-called moonshine symmetries that underlie the two-dimensional compactifications. In this paper, we embark on exploration of this connection by the free fermionic formulation to classify the symmetries of the two-dimensional heterotic–string theories. We use two complementary approaches in our classification. The first utilises a construction which is akin to the one used in the spinor–vector duality. Underlying this method is the triality property of SO(8) representations. In the second approach, we use the free fermionic tools to classify the twenty-four-dimensional Niemeier lattices.http://dx.doi.org/10.1155/2017/3572469 |
| spellingShingle | Panos Athanasopoulos Alon E. Faraggi Niemeier Lattices in the Free Fermionic Heterotic–String Formulation Advances in Mathematical Physics |
| title | Niemeier Lattices in the Free Fermionic Heterotic–String Formulation |
| title_full | Niemeier Lattices in the Free Fermionic Heterotic–String Formulation |
| title_fullStr | Niemeier Lattices in the Free Fermionic Heterotic–String Formulation |
| title_full_unstemmed | Niemeier Lattices in the Free Fermionic Heterotic–String Formulation |
| title_short | Niemeier Lattices in the Free Fermionic Heterotic–String Formulation |
| title_sort | niemeier lattices in the free fermionic heterotic string formulation |
| url | http://dx.doi.org/10.1155/2017/3572469 |
| work_keys_str_mv | AT panosathanasopoulos niemeierlatticesinthefreefermionicheteroticstringformulation AT alonefaraggi niemeierlatticesinthefreefermionicheteroticstringformulation |