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

We show how the linear special conformal transformation in four-dimensional $N=4\mathrm{}$ 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 ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ supergravity and super-Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence.