Gauged fermionic matrix quantum mechanics
Abstract We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large N limit this system describes a c = 1/2 chiral fermion in 1 + 1 dimensions. The Gauss’ law constraint implies that to obtain a physical state, indices of the fermionic matrices must be fully cont...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP03(2019)185 |
| _version_ | 1811340884631879680 |
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| author | David Berenstein Robert de Mello Koch |
| author_facet | David Berenstein Robert de Mello Koch |
| author_sort | David Berenstein |
| collection | DOAJ |
| description | Abstract We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large N limit this system describes a c = 1/2 chiral fermion in 1 + 1 dimensions. The Gauss’ law constraint implies that to obtain a physical state, indices of the fermionic matrices must be fully contracted, to form a singlet. There are two ways in which this can be achieved: one can consider a trace basis formed from products of traces of fermionic matrices or one can consider a Schur function basis, labeled by Young diagrams. The Schur polynomials for the fermions involve a twisted character, as a consequence of Fermi statistics. The main result of this paper is a proof that the trace and Schur bases coincide up to a simple normalization coefficient that we have computed. |
| first_indexed | 2024-04-13T18:49:28Z |
| format | Article |
| id | doaj.art-db119ed240b94aa88aefeaff50641816 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-13T18:49:28Z |
| publishDate | 2019-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-db119ed240b94aa88aefeaff506418162022-12-22T02:34:30ZengSpringerOpenJournal of High Energy Physics1029-84792019-03-012019311810.1007/JHEP03(2019)185Gauged fermionic matrix quantum mechanicsDavid Berenstein0Robert de Mello Koch1Department of Physics, University of CaliforniaInstitute of Quantum Matter, School of Physics and Telecommunication Engineering, South China Normal UniversityAbstract We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large N limit this system describes a c = 1/2 chiral fermion in 1 + 1 dimensions. The Gauss’ law constraint implies that to obtain a physical state, indices of the fermionic matrices must be fully contracted, to form a singlet. There are two ways in which this can be achieved: one can consider a trace basis formed from products of traces of fermionic matrices or one can consider a Schur function basis, labeled by Young diagrams. The Schur polynomials for the fermions involve a twisted character, as a consequence of Fermi statistics. The main result of this paper is a proof that the trace and Schur bases coincide up to a simple normalization coefficient that we have computed.http://link.springer.com/article/10.1007/JHEP03(2019)1851/N ExpansionAdS-CFT CorrespondenceGauge-gravity correspondence |
| spellingShingle | David Berenstein Robert de Mello Koch Gauged fermionic matrix quantum mechanics Journal of High Energy Physics 1/N Expansion AdS-CFT Correspondence Gauge-gravity correspondence |
| title | Gauged fermionic matrix quantum mechanics |
| title_full | Gauged fermionic matrix quantum mechanics |
| title_fullStr | Gauged fermionic matrix quantum mechanics |
| title_full_unstemmed | Gauged fermionic matrix quantum mechanics |
| title_short | Gauged fermionic matrix quantum mechanics |
| title_sort | gauged fermionic matrix quantum mechanics |
| topic | 1/N Expansion AdS-CFT Correspondence Gauge-gravity correspondence |
| url | http://link.springer.com/article/10.1007/JHEP03(2019)185 |
| work_keys_str_mv | AT davidberenstein gaugedfermionicmatrixquantummechanics AT robertdemellokoch gaugedfermionicmatrixquantummechanics |