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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2508.14959 |
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| _version_ | 1866915454141857792 |
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| author | D'Hoker, Eric Gutperle, Michael Uhlemann, Christoph F. |
| author_facet | D'Hoker, Eric Gutperle, Michael Uhlemann, Christoph F. |
| contents | We construct the general local solutions to complexified Type IIB supergravity which are invariant under the complexified Lie superalgebra $F(4)$. The geometry is a product of complexified maximally symmetric spaces $\mathcal M_{6 {\mathbb C}}$ and $\mathcal M_{2 {\mathbb C}}$ warped over a complexified surface $Σ_{\mathbb C}$. We classify the reality conditions that may be imposed consistently to obtain real form solutions within real forms of complex Type IIB supergravity. The latter comprise standard Type IIB, Type IIB$^\star$ and IIB$^\prime$, as well as theories with $3$, $5$, $7$ and $9$ time-like directions. Our classification of real solutions is consistent with and exhausts the real forms of $F(4)$, whose classification we confirm by elementary methods. The geometry of each real form solution is a product of real maximally symmetric spaces $\mathcal M_6$ and $\mathcal M_2$ warped over a Riemann surface $Σ$, with various signatures. The real solutions include, among others, known $AdS_6 \times S^2 \times Σ$ and $AdS_2 \times S^6 \times Σ$ solutions to standard Type IIB as well as new solutions of the form $dS_{1,5}\times S^2 \times Σ$ in Type IIB$^\star$. There are no real forms of the complex solutions with $\mathfrak{so} (7;{\mathbb R}) \oplus \mathfrak{so} (3;{\mathbb R})$ symmetry. We discuss the relevance of the complex solutions, and of analytic continuations from $dS_{1,5}\times S^2\timesΣ$ to $S^6\times S^2\timesΣ$ within complex Type IIB, in connection with holography for the polarized IKKT model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14959 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact solutions to complex Type IIB supergravity for complex superalgebra $F(4)$ and its real forms D'Hoker, Eric Gutperle, Michael Uhlemann, Christoph F. High Energy Physics - Theory We construct the general local solutions to complexified Type IIB supergravity which are invariant under the complexified Lie superalgebra $F(4)$. The geometry is a product of complexified maximally symmetric spaces $\mathcal M_{6 {\mathbb C}}$ and $\mathcal M_{2 {\mathbb C}}$ warped over a complexified surface $Σ_{\mathbb C}$. We classify the reality conditions that may be imposed consistently to obtain real form solutions within real forms of complex Type IIB supergravity. The latter comprise standard Type IIB, Type IIB$^\star$ and IIB$^\prime$, as well as theories with $3$, $5$, $7$ and $9$ time-like directions. Our classification of real solutions is consistent with and exhausts the real forms of $F(4)$, whose classification we confirm by elementary methods. The geometry of each real form solution is a product of real maximally symmetric spaces $\mathcal M_6$ and $\mathcal M_2$ warped over a Riemann surface $Σ$, with various signatures. The real solutions include, among others, known $AdS_6 \times S^2 \times Σ$ and $AdS_2 \times S^6 \times Σ$ solutions to standard Type IIB as well as new solutions of the form $dS_{1,5}\times S^2 \times Σ$ in Type IIB$^\star$. There are no real forms of the complex solutions with $\mathfrak{so} (7;{\mathbb R}) \oplus \mathfrak{so} (3;{\mathbb R})$ symmetry. We discuss the relevance of the complex solutions, and of analytic continuations from $dS_{1,5}\times S^2\timesΣ$ to $S^6\times S^2\timesΣ$ within complex Type IIB, in connection with holography for the polarized IKKT model. |
| title | Exact solutions to complex Type IIB supergravity for complex superalgebra $F(4)$ and its real forms |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.14959 |