Fermions, differential forms and doubled geometry
We show that all fermions of one generation of the Pati–Salam version of the Standard Model (SM) can be elegantly described by a single fixed parity (say even) inhomogeneous real-valued differential form in seven dimensions. In this formalism the full kinetic term of the SM fermionic Lagrangian is r...
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| Published in | Nuclear physics. B Vol. 936; pp. 36 - 75 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.11.2018
Elsevier |
| Online Access | Get full text |
| ISSN | 0550-3213 1873-1562 |
| DOI | 10.1016/j.nuclphysb.2018.09.006 |
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| Abstract | We show that all fermions of one generation of the Pati–Salam version of the Standard Model (SM) can be elegantly described by a single fixed parity (say even) inhomogeneous real-valued differential form in seven dimensions. In this formalism the full kinetic term of the SM fermionic Lagrangian is reproduced as the appropriate dimensional reduction of (Ψ,DΨ) where Ψ is a general even degree differential form in R7, the inner product (⋅,⋅) is as described in the main text, and D is essentially an appropriately interpreted exterior derivative operator. The new formalism is based on geometric constructions originating in the subjects of generalised geometry and double field theory. |
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| AbstractList | We show that all fermions of one generation of the Pati–Salam version of the Standard Model (SM) can be elegantly described by a single fixed parity (say even) inhomogeneous real-valued differential form in seven dimensions. In this formalism the full kinetic term of the SM fermionic Lagrangian is reproduced as the appropriate dimensional reduction of (Ψ,DΨ) where Ψ is a general even degree differential form in R7, the inner product (⋅,⋅) is as described in the main text, and D is essentially an appropriately interpreted exterior derivative operator. The new formalism is based on geometric constructions originating in the subjects of generalised geometry and double field theory. |
| Author | Krasnov, Kirill |
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| Cites_doi | 10.1016/j.physrep.2010.05.002 10.1016/j.physletb.2017.06.025 10.1103/PhysRevD.8.1240 10.1088/1361-6382/aac58d 10.1090/S0273-0979-10-01294-2 10.1007/BF01214659 10.1142/S0217732304013258 10.1088/1361-6382/aa8b45 10.1103/PhysRevD.47.5453 10.1103/PhysRevD.81.025010 10.1063/1.3694739 10.1093/qmath/hag025 |
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| Title | Fermions, differential forms and doubled geometry |
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