Maximally symmetric nuts in 4d \U0001d4a9 = 2 higher derivative supergravity

Abstract

We initiate a systematic study of supersymmetric backgrounds in 4d \U0001d4a9 = 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 ℝ4 and ℍ4 (Euclidean AdS4) 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, Ωℝ4, and its generalization with a cosmological constant of Martelli-Passias-Sparks, denoted Ωℍ4 (also known as the gravity dual of the U(1) × 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.