Non-holomorphic Corrections from Threebranes in F Theory

TL;DR

This paper constructs supergravity solutions dual to N=2 super Yang-Mills theories, analyzing instanton effects, flavor mass corrections, and quark-antiquark potentials within the holographic framework.

Contribution

It provides explicit supergravity backgrounds capturing instanton corrections and flavor mass effects in N=2 super Yang-Mills theories, matching field theory results.

Findings

Exact low energy effective action for SU(2) with Nf=4 flavors

Power law dependence of coupling on energy scale due to instantons

Agreement of four derivative terms with field theory expectations

Abstract

We construct solutions of type IIB supergravity dual to N=2 super Yang-Mills theories. By considering a probe moving in a background with constant coupling and an AdS_{5} component in its geometry, we are able to reproduce the exact low energy effective action for the theory with gauge group SU(2) and N_{f}=4 massless flavors. After turning on a mass for the flavors we find corrections to the AdS_{5} geometry. In addition, the coupling shows a power law dependence on the energy scale of the theory. The origin of the power law behaviour of the coupling is traced back to instanton corrections. Instanton corrections to the four derivative terms in the low energy effective action are correctly obtained from a probe analysis. By considering a Wilson loop in this geometry we are also able to compute the instanton effects on the quark-antiquark potential. Finally we consider a solution corresponding to an asymptotically free field theory. Again, the leading form of the four derivative terms in the low energy effective action are in complete agreement with field theory expectations.