Maximally symmetric nuts in 4d \(\mathcal{N} = 2\) higher derivative supergravity

DOI10.1007/JHEP02(2023)110arXiv2212.10590MaRDI QIDQ6045653

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Publication date: 12 May 2023

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Abstract: We initiate a systematic study of supersymmetric backgrounds in 4d $mathcalN=2$ Euclidean supergravity in the presence of infinite towers of higher derivative corrections. Adopting a Gibbons-Hawking view towards the evaluation of the action in terms of nuts and bolts, we consider the two maximally symmetric vacua $mathbb{R}^4$ and $mathbb{H}^4$ (Euclidean AdS${}_4$) and their unique supersymmetric deformations with (anti-) self-dual Maxwell tensors corresponding to a single nut at the center. These are the Omega background of Nekrasov-Okounkov, $Omega,mathbb{R}^4$, and its generalization with a cosmological constant of Martelli-Passias-Sparks, denoted $Omega,mathbb{H}^4$ (also known as the gravity dual of the $U(1)imesU(1)$ squashed sphere). We write down the BPS configurations in the superconformal formalism in the presence of vector multiplets and derive the corresponding off- and on-shell actions. Our results provide a rigorous proof for important parts of the conjecture in arXiv:2111.06903 and its holographic corollary in arXiv:2204.02992, which we discuss in detail along with extensions such as the addition of hypermultiplets and the presence of conical defects.

Full work available at URL: https://arxiv.org/abs/2212.10590

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