Symmetry crossover protecting chirality in Dirac spectra
Abstract We consider a random matrix model in the hard edge limit (local spectral statistics at the origin in the limit of large matrix size) which interpolates between the Gaussian unitary ensemble (GUE) and the chiral Gaussian unitary ensemble (chGUE). We show that this model is equivalent to the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2018)205 |
| _version_ | 1818546332022865920 |
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| author | Takuya Kanazawa Mario Kieburg |
| author_facet | Takuya Kanazawa Mario Kieburg |
| author_sort | Takuya Kanazawa |
| collection | DOAJ |
| description | Abstract We consider a random matrix model in the hard edge limit (local spectral statistics at the origin in the limit of large matrix size) which interpolates between the Gaussian unitary ensemble (GUE) and the chiral Gaussian unitary ensemble (chGUE). We show that this model is equivalent to the low-energy limit of certain QCD-like theories in the epsilon-regime. Moreover, we present a detailed derivation of the microscopic level density as well as the partially quenched and unquenched partition functions. Some of these results have been announced in a former letter by us. Our derivation relies on the supersymmetry method and is performed here step by step. Additionally, we compute the chiral condensate and the pion condensate for the quenched as well as unquenched settings. We also investigate the limits to GUE and chGUE and confirm our conjecture that the non-uniformity of the GUE limit would carry over to the hard edge limit. |
| first_indexed | 2024-12-12T07:51:46Z |
| format | Article |
| id | doaj.art-d7a5e51f856e4e57be0770ef35c69e24 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-12T07:51:46Z |
| publishDate | 2018-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-d7a5e51f856e4e57be0770ef35c69e242022-12-22T00:32:25ZengSpringerOpenJournal of High Energy Physics1029-84792018-11-0120181114310.1007/JHEP11(2018)205Symmetry crossover protecting chirality in Dirac spectraTakuya Kanazawa0Mario Kieburg1Research and Development Group, Hitachi, Ltd.Department of Physics, Bielefeld UniversityAbstract We consider a random matrix model in the hard edge limit (local spectral statistics at the origin in the limit of large matrix size) which interpolates between the Gaussian unitary ensemble (GUE) and the chiral Gaussian unitary ensemble (chGUE). We show that this model is equivalent to the low-energy limit of certain QCD-like theories in the epsilon-regime. Moreover, we present a detailed derivation of the microscopic level density as well as the partially quenched and unquenched partition functions. Some of these results have been announced in a former letter by us. Our derivation relies on the supersymmetry method and is performed here step by step. Additionally, we compute the chiral condensate and the pion condensate for the quenched as well as unquenched settings. We also investigate the limits to GUE and chGUE and confirm our conjecture that the non-uniformity of the GUE limit would carry over to the hard edge limit.http://link.springer.com/article/10.1007/JHEP11(2018)205Matrix ModelsChiral LagrangiansSigma ModelsSpontaneous Symmetry Breaking |
| spellingShingle | Takuya Kanazawa Mario Kieburg Symmetry crossover protecting chirality in Dirac spectra Journal of High Energy Physics Matrix Models Chiral Lagrangians Sigma Models Spontaneous Symmetry Breaking |
| title | Symmetry crossover protecting chirality in Dirac spectra |
| title_full | Symmetry crossover protecting chirality in Dirac spectra |
| title_fullStr | Symmetry crossover protecting chirality in Dirac spectra |
| title_full_unstemmed | Symmetry crossover protecting chirality in Dirac spectra |
| title_short | Symmetry crossover protecting chirality in Dirac spectra |
| title_sort | symmetry crossover protecting chirality in dirac spectra |
| topic | Matrix Models Chiral Lagrangians Sigma Models Spontaneous Symmetry Breaking |
| url | http://link.springer.com/article/10.1007/JHEP11(2018)205 |
| work_keys_str_mv | AT takuyakanazawa symmetrycrossoverprotectingchiralityindiracspectra AT mariokieburg symmetrycrossoverprotectingchiralityindiracspectra |