Symmetry Structure of ADHM Sigma Models and $AdS_3$ Superstrings

TL;DR

This paper investigates the supersymmetry structures of ADHM instanton sigma models and their relation to superconformal algebras, elucidating their flow and duality in $AdS_3$ superstring backgrounds.

Contribution

It clarifies the supersymmetry structure of ADHM sigma models and their connection to various $N=4$ superconformal algebras relevant for $AdS_3$ superstring dualities.

Findings

ADHM sigma models exhibit (0,4) supersymmetry.

Superconformal algebras relate to ADHM models and flow to each other.

Mapping of $N=4$ superconformal symmetries onto dual superstring backgrounds.

Abstract

We clarify the supersymmetry structure of ADHM instanton linear sigma models, $N=4$ superconformal algebras and superconformal field theories dual to superstrings moving in $AdS_3$ backgrounds in view of some of our recent findings in various investigations. First of all we collect information about the (0, 4) supersymmetries of Witten's original, Ali-Ilahi's complementary and Ali-Salih's complete ADHM instanton linear sigma models. Then we collect information about large, small and middle $N=4$ superconformal algebras and summarize their interrelations with the ADHM instanton linear sigma models. We then argue that the former, that is the supersymmetry of the ADHM instanton linear sigma models, flows to latter, that is the small, middle and large $N=4$ superconformal symmetries, in the infrared limit. Finally we summarize the mapping of these $N=4$ superconformal symmetries onto the superconformal symmetries dual to superstrings moving on $AdS_3\times S^3\times {\mathcal M}^4$ backgrounds with ${\mathcal M}^=K3, T^4$ and $S^3\times S^1$.