$\mathcal{N}=3$ conformal superspace in four dimensions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916097458962432 |
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| author | Kuzenko, Sergei M. Raptakis, Emmanouil S. N. |
| author_facet | Kuzenko, Sergei M. Raptakis, Emmanouil S. N. |
| contents | We develop a superspace formulation for ${\cal N}=3$ conformal supergravity in four spacetime dimensions as a gauge theory of the superconformal group $\mathsf{SU}(2,2|3)$. Upon imposing certain covariant constraints, the algebra of conformally covariant derivatives $\nabla_A = (\nabla_a,\nabla_α^i,\bar{\nabla}_i^{\dot α})$ is shown to be determined in terms of a single primary chiral spinor superfield, the super-Weyl spinor $W_α$ of dimension $+1/2$ and its conjugate. Associated with $W_α$ is its primary descendant $B^i{}_j$ of dimension $+2$, the super-Bach tensor, which determines the equation of motion for conformal supergravity. As an application of this construction, we present two different but equivalent action principles for ${\cal N}=3$ conformal supergravity. We describe the model for linearised $\mathcal{N}=3$ conformal supergravity in an arbitrary conformally flat background and demonstrate that it possesses $\mathsf{U}(1)$ duality invariance. Additionally, upon degauging certain local symmetries, our superspace geometry is shown to reduce to the $\mathsf{U}(3)$ superspace constructed by Howe more than four decades ago. Further degauging proves to lead to a new superspace formalism, called $\mathsf{SU}(3) $ superspace, which can also be used to describe ${\mathcal N}=3$ conformal supergravity. Our conformal superspace setting opens up the possibility to formulate the dynamics of the off-shell ${\mathcal N}=3$ super Yang-Mills theory coupled to conformal supergravity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_07242 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $\mathcal{N}=3$ conformal superspace in four dimensions Kuzenko, Sergei M. Raptakis, Emmanouil S. N. High Energy Physics - Theory Mathematical Physics We develop a superspace formulation for ${\cal N}=3$ conformal supergravity in four spacetime dimensions as a gauge theory of the superconformal group $\mathsf{SU}(2,2|3)$. Upon imposing certain covariant constraints, the algebra of conformally covariant derivatives $\nabla_A = (\nabla_a,\nabla_α^i,\bar{\nabla}_i^{\dot α})$ is shown to be determined in terms of a single primary chiral spinor superfield, the super-Weyl spinor $W_α$ of dimension $+1/2$ and its conjugate. Associated with $W_α$ is its primary descendant $B^i{}_j$ of dimension $+2$, the super-Bach tensor, which determines the equation of motion for conformal supergravity. As an application of this construction, we present two different but equivalent action principles for ${\cal N}=3$ conformal supergravity. We describe the model for linearised $\mathcal{N}=3$ conformal supergravity in an arbitrary conformally flat background and demonstrate that it possesses $\mathsf{U}(1)$ duality invariance. Additionally, upon degauging certain local symmetries, our superspace geometry is shown to reduce to the $\mathsf{U}(3)$ superspace constructed by Howe more than four decades ago. Further degauging proves to lead to a new superspace formalism, called $\mathsf{SU}(3) $ superspace, which can also be used to describe ${\mathcal N}=3$ conformal supergravity. Our conformal superspace setting opens up the possibility to formulate the dynamics of the off-shell ${\mathcal N}=3$ super Yang-Mills theory coupled to conformal supergravity. |
| title | $\mathcal{N}=3$ conformal superspace in four dimensions |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2312.07242 |