A Lattice Non-Perturbative Definition of an SO(10) Chiral Gauge Theory and Its Induced Standard Model
The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently. The standard model is defined perturbatively and describes all elementary particles (except gravitons) very well. However, for a long time, we do not know if we can hav...
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| Format: | Article |
| Language: | en_US |
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IOP Publishing
2014
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| Online Access: | http://hdl.handle.net/1721.1/88586 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826197734133071872 |
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| author | Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang |
| author_sort | Wen, Xiao-Gang |
| collection | MIT |
| description | The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently. The standard model is defined perturbatively and describes all elementary particles (except gravitons) very well. However, for a long time, we do not know if we can have a non-perturbative definition of the standard model as a Hamiltonian quantum mechanical theory. Here we propose a way to give a modified standard model (with 48 two-component Weyl fermions) a non-perturbative definition by embedding the modified standard model into an SO (10) chiral gauge theory. We show that the SO (10) chiral gauge theory can be put on a lattice (a 3D spatial lattice with a continuous time) if we allow fermions to interact. Such a non-perturbatively defined standard model is a Hamiltonian quantum theory with a finite-dimensional Hilbert space for a finite space volume. More generally, using the defining connection between gauge anomalies and the symmetry-protected topological orders, one can show that any truly anomaly-free chiral gauge theory can be non-perturbatively defined by putting it on a lattice in the same dimension. |
| first_indexed | 2024-09-23T10:52:37Z |
| format | Article |
| id | mit-1721.1/88586 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:52:37Z |
| publishDate | 2014 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/885862022-09-30T23:36:15Z A Lattice Non-Perturbative Definition of an SO(10) Chiral Gauge Theory and Its Induced Standard Model Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently. The standard model is defined perturbatively and describes all elementary particles (except gravitons) very well. However, for a long time, we do not know if we can have a non-perturbative definition of the standard model as a Hamiltonian quantum mechanical theory. Here we propose a way to give a modified standard model (with 48 two-component Weyl fermions) a non-perturbative definition by embedding the modified standard model into an SO (10) chiral gauge theory. We show that the SO (10) chiral gauge theory can be put on a lattice (a 3D spatial lattice with a continuous time) if we allow fermions to interact. Such a non-perturbatively defined standard model is a Hamiltonian quantum theory with a finite-dimensional Hilbert space for a finite space volume. More generally, using the defining connection between gauge anomalies and the symmetry-protected topological orders, one can show that any truly anomaly-free chiral gauge theory can be non-perturbatively defined by putting it on a lattice in the same dimension. National Science Foundation (U.S.) (Grant DMR-1005541) 2014-08-07T16:34:10Z 2014-08-07T16:34:10Z 2013-11 2013-10 Article http://purl.org/eprint/type/JournalArticle 0256-307X 1741-3540 http://hdl.handle.net/1721.1/88586 Wen, Xiao-Gang. “ A Lattice Non-Perturbative Definition of an SO (10) Chiral Gauge Theory and Its Induced Standard Model .” Chinese Phys. Lett. 30, no. 11 (November 2013): 111101. https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1088/0256-307x/30/11/111101 Chinese Physics Letters Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf IOP Publishing arXiv |
| spellingShingle | Wen, Xiao-Gang A Lattice Non-Perturbative Definition of an SO(10) Chiral Gauge Theory and Its Induced Standard Model |
| title | A Lattice Non-Perturbative Definition of an SO(10) Chiral Gauge Theory and Its Induced Standard Model |
| title_full | A Lattice Non-Perturbative Definition of an SO(10) Chiral Gauge Theory and Its Induced Standard Model |
| title_fullStr | A Lattice Non-Perturbative Definition of an SO(10) Chiral Gauge Theory and Its Induced Standard Model |
| title_full_unstemmed | A Lattice Non-Perturbative Definition of an SO(10) Chiral Gauge Theory and Its Induced Standard Model |
| title_short | A Lattice Non-Perturbative Definition of an SO(10) Chiral Gauge Theory and Its Induced Standard Model |
| title_sort | lattice non perturbative definition of an so 10 chiral gauge theory and its induced standard model |
| url | http://hdl.handle.net/1721.1/88586 https://orcid.org/0000-0002-5874-581X |
| work_keys_str_mv | AT wenxiaogang alatticenonperturbativedefinitionofanso10chiralgaugetheoryanditsinducedstandardmodel AT wenxiaogang latticenonperturbativedefinitionofanso10chiralgaugetheoryanditsinducedstandardmodel |