# Holographic Aspects of Four Dimensional ${\cal N }=2$ SCFTs and their Marginal Deformations

## TL;DR

This paper explores the holographic duals of four-dimensional ${
m extbf{N}}=2$ superconformal field theories, deriving new formulas for key observables and extending the analysis to marginal deformations, revealing an infinite family of solutions.

## Contribution

It introduces new holographic expressions for characteristic numbers and central charges of ${
m extbf{N}}=2$ SCFTs, including their marginal deformations, based on solving a Laplace equation.

## Key findings

- Derived new holographic formulas for characteristic numbers and central charges.
- Constructed an infinite family of solutions for marginally deformed theories.
- Validated the new expressions through multiple examples and proofs.

## Abstract

We study the holographic description of ${\cal N}=2$ Super Conformal Field Theories in four dimensions first given by Gaiotto and Maldacena. We present new expressions that holographically calculate characteristic numbers of the CFT and associated Hanany-Witten set-ups, or more dynamical observables, like the central charge. A number of examples of varying complexity are studied and some proofs for these new expressions are presented. We repeat this treatment for the case of the marginally deformed Gaiotto-Maldacena theories, presenting an infinite family of new solutions and compute some of its observables. These new backgrounds rely on the solution of a Laplace equation and a boundary condition, encoding the kinematics of the original conformal field theory.