D-instanton probes of N=2 non-conformal geometries

TL;DR

The paper develops a D-instanton probe framework for non-conformal ${\cal N}=2$ theories arising from D3-branes on orbifolds ${\mathbb R}^4/{\mathbb Z}_p$, linking finite-$N$ instanton calculus to holographic geometry and RG data. By projecting onto fractional and regular sectors, it shows a per-node one-loop beta-function consistent with field theory and identifies a deformed $AdS_5\times S^1$ geometry for fractional branes, while regular branes probe a conformal $AdS_5\times S^5/{\mathbb Z}_p$ geometry. The D-instanton action is reformulated as a topological (cohomological) theory with BRST-like symmetry, enabling localization and a deeper connection between ADHM moduli and holographic backgrounds, including the presence of fundamental matter. The work further extends to instantons on ALE spaces, illustrating how Kronheimer–Nakajima data affects moduli and geometry, and highlighting the broader relevance of D-instanton probes for non-conformal holography and mathematical structures of instanton moduli spaces.

Abstract

D-instanton calculus has proved to be able to probe the AdS near horizon geometry for $N$ D-branes systems which, when decoupled from gravity, yield four dimensional superconformal gauge theories with various matter content. In this work we extend previous analysis to encompass fractional brane models which give rise to non conformal N=2 Super Yang-Mills theories. Via D-instanton calculus we study the geometry of such models for finite $N$ and recover the $β$ function of the gauge coupling constants which is expected in non conformal gauge theories. We also give a topological matrix theory formulation for the D-instanton action of these theories. Finally, we revisit the related system where the D3-branes wrap a ${\real}^4/{\zet}_p$ orbifold singularity and the D(-1) branes are associated to instanton solutions of four-dimensional gauge theories in the blown down ALE space.