Three Brane Action and The Correspondence Between N=4 Yang Mills Theory and Anti De Sitter Space

TL;DR

This paper investigates the AdS/CFT correspondence by analyzing the D3 brane action, demonstrating how supergravity modes relate to operators in N=4 Super Yang Mills theory, especially focusing on two-form gauge fields and their associated operators.

Contribution

It shows that the leading operator in the Yang Mills theory corresponding to supergravity modes can be derived from the D3 brane Dirac-Born-Infeld and Wess-Zumino actions expanded around AdS background.

Findings

The operator with dimension six matches supergravity predictions.

The Wess-Zumino term cancels lower dimension operators.

The analysis confirms the operator-mode correspondence in the D3 brane framework.

Abstract

Recently, a relation between N=4 Super Yang Mills in 3+1 dimensions and supergravity in an $AdS_5$ background has been proposed. In this paper we explore the idea that the correspondence between operators in the Yang Mills theory and modes of the supergravity theory can be obtained by using the D3 brane action. Specifically, we consider two form gauge fields for this purpose. The supergravity analysis predicts that the operator which corresponds to this mode has dimension six. We show that this is indeed the leading operator in the three brane Dirac-Born-Infeld and Wess-Zumino action which couples to this mode. It is important in the analysis that the brane action is expanded around the anti de-Sitter background. Also, the Wess-Zumino term plays a crucial role in cancelling a lower dimension operator which appears in the the Dirac-Born-Infeld action.