# Holography for field theory solitons

## TL;DR

This paper extends the AdS/dCFT holographic framework to non-abelian defects, analyzing a dual description involving gravity and supersymmetric Yang-Mills theories on curved backgrounds, and explores solitons and truncations.

## Contribution

It introduces a non-abelian defect construction in holography, studies supersymmetric Yang-Mills theories on AdS_4 x S^2, and demonstrates consistent truncations and soliton solutions.

## Key findings

- Existence of a decoupled gravity and Yang-Mills sector in the low-energy regime.
- Supersymmetric Yang-Mills theories on curved backgrounds with varying supersymmetries.
- Identification of BPS solitons and consistent truncations on the two-sphere.

## Abstract

We extend a well-known D-brane construction of the AdS/dCFT correspondence to non-abelian defects. We focus on the bulk side of the correspondence and show that there exists a regime of parameters in which the low-energy description consists of two approximately decoupled sectors. The two sectors are gravity in the ambient spacetime, and a six-dimensional supersymmetric Yang-Mills theory. The Yang-Mills theory is defined on a rigid AdS_4 x S^2 background and admits sixteen supersymmetries. We also consider a one-parameter deformation that gives rise to a family of Yang-Mills theories on asymptotically AdS_4 x S^2 spacetimes, which are invariant under eight supersymmetries. With future holographic applications in mind, we analyze the vacuum structure and perturbative spectrum of the Yang-Mills theory on AdS_4 x S^2, as well as systems of BPS equations for finite-energy solitons. Finally, we demonstrate that the classical Yang-Mills theory has a consistent truncation on the two-sphere, resulting in maximally supersymmetric Yang-Mills on AdS_4.