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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.14668 |
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| _version_ | 1866914567223771136 |
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| author | Cerdeira, José Luis V. Corral, Cristóbal Ortín, Tomás |
| author_facet | Cerdeira, José Luis V. Corral, Cristóbal Ortín, Tomás |
| contents | We study the $α'$ corrections to self-dual gravitational instantons in the context of the four-dimensional Cano--Ruipérez action, which can be obtained by the compactification of the Bergshoeff--de Roo heterotic string effective action on $\mathbb{T}^{6}$ followed by a truncation and a field redefinition. We show that the metric of spaces of self-dual curvature does not receive any corrections, but their (initially trivial) dilaton and axion fields do, owing to their couplings to Gauss--Bonnet and Pontrjagin densities. We find the generic form of the corrections of the dilaton and axion fields for the Gibbons--Hawking multi-instanton solutions and their explicit form for the particular cases of the Euclidean Taub--NUT and Eguchi--Hanson spaces. We construct the boundary terms required to define a well-posed Dirichlet variational principle in the Euclidean Cano--Ruipérez theory, including the contributions associated with the Gauss--Bonnet and Pontrjagin terms. The boundary terms are normalized for asymptotically-locally-Euclidean solutions, and we evaluate with them the Euclidean action of the $α'$-corrected Eguchi--Hanson instanton showing that the total action receives no corrections to first order in $α'$. We also show that, at zeroth order in $α'$, one can construct Euclidean solutions similar to the string theory D-instanton with non-trivial dilaton and axion on the background of a self-dual purely gravitational instanton which remains unmodified. We also compute the $α'$ corrections to these solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14668 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $α'$ corrections to self-dual gravitational instantons Cerdeira, José Luis V. Corral, Cristóbal Ortín, Tomás High Energy Physics - Theory General Relativity and Quantum Cosmology We study the $α'$ corrections to self-dual gravitational instantons in the context of the four-dimensional Cano--Ruipérez action, which can be obtained by the compactification of the Bergshoeff--de Roo heterotic string effective action on $\mathbb{T}^{6}$ followed by a truncation and a field redefinition. We show that the metric of spaces of self-dual curvature does not receive any corrections, but their (initially trivial) dilaton and axion fields do, owing to their couplings to Gauss--Bonnet and Pontrjagin densities. We find the generic form of the corrections of the dilaton and axion fields for the Gibbons--Hawking multi-instanton solutions and their explicit form for the particular cases of the Euclidean Taub--NUT and Eguchi--Hanson spaces. We construct the boundary terms required to define a well-posed Dirichlet variational principle in the Euclidean Cano--Ruipérez theory, including the contributions associated with the Gauss--Bonnet and Pontrjagin terms. The boundary terms are normalized for asymptotically-locally-Euclidean solutions, and we evaluate with them the Euclidean action of the $α'$-corrected Eguchi--Hanson instanton showing that the total action receives no corrections to first order in $α'$. We also show that, at zeroth order in $α'$, one can construct Euclidean solutions similar to the string theory D-instanton with non-trivial dilaton and axion on the background of a self-dual purely gravitational instanton which remains unmodified. We also compute the $α'$ corrections to these solutions. |
| title | $α'$ corrections to self-dual gravitational instantons |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.14668 |