ADHM and D-instantons in orbifold AdS/CFT duality

TL;DR

This paper explores the role of ADHM instantons in orbifold AdS/CFT duality, demonstrating how D-instanton dynamics relate to gauge theory instantons and their behavior in smooth versus singular orbifold geometries.

Contribution

It provides a detailed analysis of ADHM instantons in orbifold gauge theories and connects their collective coordinate measures to D-instanton partition functions in dual AdS backgrounds, including singular cases.

Findings

Saddle-point solutions exist only when instanton charges are equal in smooth orbifolds.

In singular orbifolds, instanton charges can differ, leading to multiple solution branches.

D-instantons in type 0B duals exhibit two distinct solution types.

Abstract

We consider ADHM instantons in product group gauge theories that arise from D3-branes located at points in the orbifold R^6/Z_p. At finite N we argue that the ADHM construction and collective coordinate integration measure can be deduced from the dynamics of D-instantons in the D3-brane background. For the large-N conformal field theories of this type, we compute a saddle-point approximation of the ADHM integration measure and show that it is proportional to the partition function of D-instantons in the dual AdS_5 x S^5/Z_p background, in agreement with the orbifold AdS/CFT correspondence. Matching the expected behaviour of D-instantons, we find that when S^5/Z_p is smooth a saddle-point solution only exists in the sector where the instanton charges in each gauge group factor are the same. However, when S^5/Z_p is singular, the instanton charges at large N need not be the same and the space of saddle-point solutions has a number of distinct branches which represent the possible fractionations of D-instantons at the singularity. For the theories with a type 0B dual the saddle-point solutions manifest two types of D-instantons.