# Topological AdS/CFT and the $\Omega$ deformation

## TL;DR

This paper develops a holographic dual framework for 4D superconformal field theories on Riemannian manifolds with symmetries, analyzing how the supergravity action varies with boundary metric deformations.

## Contribution

It introduces a new holographic dual for superconformal theories on arbitrary Riemannian manifolds with Killing vectors and studies the action variation under boundary metric changes.

## Key findings

- Defined a holographic dual for superconformal theories on manifolds with isometries.
- Analyzed the variation of the supergravity action with respect to boundary metric deformations.
- Provided insights into the geometric structure of holographic duals with symmetries.

## Abstract

In this note, we define a holographic dual to four-dimensional superconformal field theories formulated on arbitrary Riemannian manifolds equipped with a Killing vector. Moreover, assuming smoothness of the bulk solution, we study the variation of the holographically renormalized supergravity action in the class of metrics on the boundary four-manifold with a prescribed isometry.