Quantum Metamorphosis of Conformal Transformation in D3-Brane Yang-Mills Theory

TL;DR

This paper demonstrates how conformal transformations in N=4 super Yang-Mills theory correspond to nonlinear, field-dependent transformations of D3-brane coordinates, supporting the AdS/CFT correspondence.

Contribution

It reveals the metamorphosis of conformal transformations into nonlinear forms for D3-brane coordinates, strengthening the AdS/CFT duality understanding.

Findings

Conformal transformations become nonlinear for D3-brane coordinates.

Supports the AdS/CFT correspondence through transformation law analysis.

Provides insights into the nature of the AdS/SYM duality.

Abstract

We show how the linear special conformal transformation in four-dimensional N=4 super Yang-Mills theory is metamorphosed into the nonlinear and field-dependent transformation for the collective coordinates of Dirichlet 3-branes, which agrees with the transformation law for the space-time coordinates in the anti-de Sitter (AdS) space-time. Our result provides a new and strong support for the conjectured relation between AdS supergravity and super conformal Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence.