The Non-Perturbative ${\cal N} = 2 $ SUSY Yang-Mills Theory from Semiclassical Absorption of Supergravity by Wrapped D Branes

TL;DR

This paper derives the exact pre-potential of ${ m N}=2$ SUSY Yang-Mills theory using semiclassical supergravity absorption calculations, linking anomalies and the WDVV equation.

Contribution

It establishes a novel connection between semiclassical supergravity absorption, anomaly Ward identities, and the exact pre-potential in ${ m N}=2$ SUSY Yang-Mills theory.

Findings

Exact pre-potential derived from supergravity absorption data.

Relation between anomalies and the vacuum structure of the theory.

Solution of the WDVV equation for the pre-potential.

Abstract

The imaginary part of the two point functions of the superconformal anomalous currents are extracted from the cross-sections of semiclassical absorption of dilaton, RR-2 form and gravitino by the wrapped D5 branes. From the central terms of the two point functions anomalous Ward identity is established which relates the exact pre-potential of the ${\cal N}=2$ SUSY Yang-Mills theory with the vacuum expectation value of the anomaly multiplet. From the Ward identity, WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equation can be derived which is solved for the exact pre-potential.