Maximally symmetric nuts in 4d N=2 higher derivative supergravity

We initiate a systematic study of supersymmetric backgrounds in 4d N = 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 R-4 and 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 R-4, and its generalization with a cosmological constant of Martelli-Passias-Sparks, denoted Omega H-4 (also known as the gravity dual of the U(1) x U(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 [1] and its holographic corollary in [2], which we discuss in detail along with extensions such as the addition of hypermultiplets and the presence of conical defects.

Automated summary

We conduct a systematic study on supersymmetric backgrounds in 4d N = 2 Euclidean supergravity with infinite higher derivative corrections. By adopting a Gibbons-Hawking approach, we examine the action evaluation of nuts and bolts for the two maximally symmetric vacua R-4 and H-4 (Euclidean AdS(4)), as well as their unique supersymmetric deformations with (anti-)self-dual Maxwell tensors corresponding to a single nut at the center. Our research provides a rigorous proof for significant parts of the conjecture in [1] and its holographic corollary in [2], with discussions on extensions including the addition of hypermultiplets and the presence of conical defects.