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

TL;DR

This paper extends D-instanton calculus to analyze non-conformal N=2 super Yang-Mills theories derived from fractional brane models, recovering the gauge coupling beta function and providing a topological matrix theory formulation.

Contribution

It introduces a novel application of D-instanton calculus to non-conformal N=2 theories and develops a topological matrix model for the D-instanton action.

Findings

Recovered the beta function for gauge couplings in non-conformal models

Extended D-instanton analysis to fractional brane systems

Provided a topological matrix theory formulation for D-instanton actions

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 $\beta$ 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.