Field Theory for Superconducting Branes and Generalized Particle-Vortex Duality
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| Format: | Preprint |
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2024
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| _version_ | 1866916277223686144 |
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| author | Kawana, Kiyoharu |
| author_facet | Kawana, Kiyoharu |
| contents | We propose a field theory of closed $p$-brane $C_p^{}$ interacting with a $(p+1)$-form gauge field $A_{p+1}^{}$. This is a generalization of the Ginzburg-Landau theory (Abelian-Higgs model) for superconducting particles to higher-dimensional superconducting branes. A higher-form gauge invariant action is constructed by utilizing the Area derivative, which is a higher-dimensional generalization of the ordinary derivative. We find that the fundamental phenomena of superconductivity, such as the Meisser effect, topological defects, topological order, are naturally extended in the brane-field theory. We explicitly construct a topologically non-trivial static configuration that is characterized by the first homotopy group. Then, we calculate the low-energy effective theory in the presence of the topological defect and find that it is described by a BF-type topological field theory coupled with the world-volume of the topological defect. We also conjecture an infra-red duality between the superconducting brane-field model and dual brane-field model with a global $\mathrm{U}(1)$ higher-form symmetry as a generalization of the Particle-Vortex duality. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_03670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Field Theory for Superconducting Branes and Generalized Particle-Vortex Duality Kawana, Kiyoharu High Energy Physics - Theory Superconductivity We propose a field theory of closed $p$-brane $C_p^{}$ interacting with a $(p+1)$-form gauge field $A_{p+1}^{}$. This is a generalization of the Ginzburg-Landau theory (Abelian-Higgs model) for superconducting particles to higher-dimensional superconducting branes. A higher-form gauge invariant action is constructed by utilizing the Area derivative, which is a higher-dimensional generalization of the ordinary derivative. We find that the fundamental phenomena of superconductivity, such as the Meisser effect, topological defects, topological order, are naturally extended in the brane-field theory. We explicitly construct a topologically non-trivial static configuration that is characterized by the first homotopy group. Then, we calculate the low-energy effective theory in the presence of the topological defect and find that it is described by a BF-type topological field theory coupled with the world-volume of the topological defect. We also conjecture an infra-red duality between the superconducting brane-field model and dual brane-field model with a global $\mathrm{U}(1)$ higher-form symmetry as a generalization of the Particle-Vortex duality. |
| title | Field Theory for Superconducting Branes and Generalized Particle-Vortex Duality |
| topic | High Energy Physics - Theory Superconductivity |
| url | https://arxiv.org/abs/2406.03670 |