Gauge/Gravity Duality, Green Functions of N=2 SYM and Radial/Energy-Scale Relation

TL;DR

This paper uses supergravity configurations of wrapped D5 branes to compute Green functions in N=2 super Yang-Mills theory, revealing perturbative and non-perturbative contributions, and establishes a radial/energy-scale relation consistent with the known beta-function.

Contribution

It provides a detailed calculation of Green functions in N=2 SYM from supergravity and derives a radial/energy-scale relation that reproduces the correct beta-function.

Findings

Green functions contain perturbative and instanton effects.

Derived radial/energy-scale relation matches known beta-function.

Supergravity captures non-perturbative instanton contributions.

Abstract

We consider supergravity configuration of D5 branes wrapped on supersymmetric 2-cycles and use it to calculate one-point and two-point Green functions of some special operators in N=2 super Yang-Mills theory. We show that Green functions obtained from supergravity include two very different parts. One of them corresponds to perturbative results of quantum field theory, and another is a non-perturbative effect which corresponds to contribution from instantons with fractional charge. Comparing Green functions obtained from supergravity and gauge theory, we obtain radial/energy-scale relation for this gauge/gravity correspondence with N=2 supersymmetry. This relation leads right beta-function of N=2 SYM from supergravity configuration.