A $3D$ Field-Theoretic Model: Discrete Duality Symmetry
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| Format: | Preprint |
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2024
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| author | Kumar, R. Malik, R. P. |
| author_facet | Kumar, R. Malik, R. P. |
| contents | We demonstrate the discrete duality symmetry between the Abelian 1-form and 2-form basic gauge fields in the context of a three $(2 + 1)$-dimensional ($3D$) combined system of the field-theoretic model of the free Abelian 1-from and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The classical gauge-fixed Lagrangian density of this theory is generalized to its quantum counterpart as the BRST and co-BRST invariant Lagrangian density. We show clearly the existence of the off-shell nilpotent (co-)BRST symmetry transformations and establish their intimate connection through a set of underlying discrete duality symmetry transformations in our $3D$ BRST-quantized theory. We provide the mathematical basis for the existence of the discrete duality symmetry transformations in our theory through the Hodge duality operator (that is defined on the $3D$ flat Minkowskian spacetime manifold). We briefly mention a bosonic symmetry transformation which is constructed from the anticommutator of the above off-shell nilpotent (co-)BRST symmetry transformations. We lay emphasis on the algebraic structures of the existing continuous and discrete duality symmetry transformations for our $3D$ BRST-quantized theory (where they are treated as operators). We also comment on the appearance of a pseudo-scalar field (with negative kinetic term). This field happens to be one of the possible candidates for the phantom field of the cosmological models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_07849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A $3D$ Field-Theoretic Model: Discrete Duality Symmetry Kumar, R. Malik, R. P. High Energy Physics - Theory We demonstrate the discrete duality symmetry between the Abelian 1-form and 2-form basic gauge fields in the context of a three $(2 + 1)$-dimensional ($3D$) combined system of the field-theoretic model of the free Abelian 1-from and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The classical gauge-fixed Lagrangian density of this theory is generalized to its quantum counterpart as the BRST and co-BRST invariant Lagrangian density. We show clearly the existence of the off-shell nilpotent (co-)BRST symmetry transformations and establish their intimate connection through a set of underlying discrete duality symmetry transformations in our $3D$ BRST-quantized theory. We provide the mathematical basis for the existence of the discrete duality symmetry transformations in our theory through the Hodge duality operator (that is defined on the $3D$ flat Minkowskian spacetime manifold). We briefly mention a bosonic symmetry transformation which is constructed from the anticommutator of the above off-shell nilpotent (co-)BRST symmetry transformations. We lay emphasis on the algebraic structures of the existing continuous and discrete duality symmetry transformations for our $3D$ BRST-quantized theory (where they are treated as operators). We also comment on the appearance of a pseudo-scalar field (with negative kinetic term). This field happens to be one of the possible candidates for the phantom field of the cosmological models. |
| title | A $3D$ Field-Theoretic Model: Discrete Duality Symmetry |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.07849 |