Isometries of a D3-brane space

TL;DR

This paper derives the isometries of a ten-dimensional D3-brane space, showing how it simplifies to AdS5×S5 in a certain limit and illustrating the correspondence between AdS isometries and boundary conformal symmetries.

Contribution

It provides explicit Killing equations and infinitesimal isometries for the D3-brane space and demonstrates the isomorphism with the boundary conformal group in the AdS/CFT context.

Findings

Derived Killing equations for D3-brane space

Showed the AdS5×S5 limit and its symmetries

Established the isomorphism between AdS isometries and conformal group

Abstract

We obtain the Killing equations and the corresponding infinitesimal isometries for the ten dimensional space generated by a large number of coincident D3-branes. In a convenient limit this space becomes an $AdS_5\times S^5$ which is relevant for the AdS/CFT correspondence. In this case, using Poincare coordinates, we also write down the Killing equations and infinitesimal isometries. Then we obtain a simple realization of the isomorphism between $AdS$ isometries and the boundary conformal group.