# The Holographic Dual of the $\Omega$-background

## TL;DR

This paper constructs an explicit supergravity background that is holographically dual to the $
abla$-deformation of a 4D $
abla$-SCFT, revealing new insights into the gauge/gravity correspondence with preserved supersymmetry.

## Contribution

It provides the first explicit supergravity solution dual to the $
abla$-deformation of a 4D $
abla$-SCFT, including its uplift to type IIB supergravity with preserved supersymmetry.

## Key findings

- Explicit supergravity background dual to the $
abla$-deformation.
- Uplift to type IIB supergravity as a deformation of AdS$_5\times S^5$.
- Preserves 16 supercharges.

## Abstract

We find an explicit supergravity background dual to the $\Omega$-deformation of a four-dimensional $\mathcal{N}=2$ SCFT on $\mathbb{R}^4$. The solution can be constructed in the five-dimensional ${\cal N}=4^+$ gauged supergravity and has a nontrivial self-dual 2-form. When uplifted to type IIB supergravity the background is a deformation of AdS$_5\times S^5$ which preserves 16 supercharges. We also discuss generalizations of this solution corresponding to turning on a vacuum expectation value for a scalar operator in the dual SCFT.