<i>Q</i>-Form Field on a <i>p</i>-Brane with Codimension Two
This paper investigates gauge invariance in a bulk massless q-form field on a p-brane with codimension two, utilizing a general Kaluza–Klein (KK) decomposition. The KK decomposition analysis reveals four distinct KK modes: the conventional <i>q</i>-form, two <inline-formula><mat...
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MDPI AG
2023-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/10/1819 |
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| author | Ziqi Chen Chun’e Fu Xiaoyu Zhang Chen Yang Li Zhao |
| author_facet | Ziqi Chen Chun’e Fu Xiaoyu Zhang Chen Yang Li Zhao |
| author_sort | Ziqi Chen |
| collection | DOAJ |
| description | This paper investigates gauge invariance in a bulk massless q-form field on a p-brane with codimension two, utilizing a general Kaluza–Klein (KK) decomposition. The KK decomposition analysis reveals four distinct KK modes: the conventional <i>q</i>-form, two <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-forms and one <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>-form. These diverse modes are essential for maintaining gauge invariance. We also find eight Schrödinger-like equations for the four modes due to the two extra dimensions, and their mass spectra are closely related. The KK decomposition process gives rise to four dualities on the p-brane, originating from the inherent Hodge duality present in the bulk. Notably, these dual symmetries play a significant role in maintaining the equivalence of bulk dual fields during dimensional reduction. |
| first_indexed | 2024-03-10T20:51:48Z |
| format | Article |
| id | doaj.art-68f5ab712f784c4d8feb949a65750aba |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:51:48Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-68f5ab712f784c4d8feb949a65750aba2023-11-19T18:17:11ZengMDPI AGSymmetry2073-89942023-09-011510181910.3390/sym15101819<i>Q</i>-Form Field on a <i>p</i>-Brane with Codimension TwoZiqi Chen0Chun’e Fu1Xiaoyu Zhang2Chen Yang3Li Zhao4Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, ChinaSchool of Science, Xi’an Jiaotong University, Xi’an 710049, ChinaInstitute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, ChinaInstitute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, ChinaInstitute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, ChinaThis paper investigates gauge invariance in a bulk massless q-form field on a p-brane with codimension two, utilizing a general Kaluza–Klein (KK) decomposition. The KK decomposition analysis reveals four distinct KK modes: the conventional <i>q</i>-form, two <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-forms and one <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>-form. These diverse modes are essential for maintaining gauge invariance. We also find eight Schrödinger-like equations for the four modes due to the two extra dimensions, and their mass spectra are closely related. The KK decomposition process gives rise to four dualities on the p-brane, originating from the inherent Hodge duality present in the bulk. Notably, these dual symmetries play a significant role in maintaining the equivalence of bulk dual fields during dimensional reduction.https://www.mdpi.com/2073-8994/15/10/1819<i>q</i>-form field<i>p</i>-branelocalizationKaluza–Klein decompositionHodge duality |
| spellingShingle | Ziqi Chen Chun’e Fu Xiaoyu Zhang Chen Yang Li Zhao <i>Q</i>-Form Field on a <i>p</i>-Brane with Codimension Two Symmetry <i>q</i>-form field <i>p</i>-brane localization Kaluza–Klein decomposition Hodge duality |
| title | <i>Q</i>-Form Field on a <i>p</i>-Brane with Codimension Two |
| title_full | <i>Q</i>-Form Field on a <i>p</i>-Brane with Codimension Two |
| title_fullStr | <i>Q</i>-Form Field on a <i>p</i>-Brane with Codimension Two |
| title_full_unstemmed | <i>Q</i>-Form Field on a <i>p</i>-Brane with Codimension Two |
| title_short | <i>Q</i>-Form Field on a <i>p</i>-Brane with Codimension Two |
| title_sort | i q i form field on a i p i brane with codimension two |
| topic | <i>q</i>-form field <i>p</i>-brane localization Kaluza–Klein decomposition Hodge duality |
| url | https://www.mdpi.com/2073-8994/15/10/1819 |
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