Supersymmetric Nonlinear Sigma Model in AdS_5

TL;DR

This paper constructs a supersymmetric nonlinear sigma model in AdS_5, revealing that hyper-Kahler target spaces with specific Killing vectors are required, and explores boundary conditions linking bulk hypermultiplets to brane chiral multiplets.

Contribution

It introduces a new formulation of the supersymmetric sigma model in AdS_5 with specific geometric conditions and boundary mappings between bulk and brane fields.

Findings

Hyper-Kahler manifolds with special Killing vectors are necessary.

Boundary conditions relate bulk hypermultiplets to brane chiral multiplets.

AdS_5 isometries reduce to superconformal transformations on the brane.

Abstract

We construct the supersymmetric nonlinear sigma model in a fixed AdS_5 background. We use component fields and find that the complex bosons must be the coordinates of a hyper-Kahler manifold that admits a Killing vector satisfying an inhomogeneous tri-holomorphic condition. We propose boundary conditions that map the on-shell bulk hypermultiplets into off-shell chiral multiplets on 3-branes that foliate the bulk. The supersymmetric AdS_5 isometries reduce to superconformal transformations on the brane fields.