Generalized Conformal Symmetry in D-Brane Matrix Models

TL;DR

This paper demonstrates the existence of generalized conformal symmetry in supersymmetric Yang-Mills matrix models of Dp-branes, extending previous work and providing tools to restrict D-brane effective actions and configurations.

Contribution

It extends the concept of generalized conformal symmetry to Dp-brane matrix models for arbitrary p, including derivation of field-dependent transformations and their supergravity correspondence.

Findings

Confirmed symmetry exists in both Yang-Mills and supergravity backgrounds.

Derived one-loop level field-dependent conformal transformations.

Extended symmetry concept to arbitrary D-brane configurations.

Abstract

We study in detail the extension of the generalized conformal symmetry proposed previously for D-particles to the case of supersymmetric Yang-Mills matrix models of Dp-branes for arbitrary p. It is demonstrated that such a symmetry indeed exists both in the Yang-Mills theory and in the corresponding supergravity backgrounds produced by Dp-branes. On the Yang-Mills side, we derive the field-dependent special conformal transformations for the collective coordinates of Dp-branes in the one-loop approximation, and show that they coincide with the transformations on the supergravity side. These transformations are powerful in restricting the forms of the effective actions of probe D-branes in the fixed backgrounds of source D-branes. Furthermore, our formalism enables us to extend the concept of (generalized) conformal symmetry to arbitrary configurations of D-branes, which can still be used to restrict the dynamics of D-branes. For such general configurations, however, it cannot be endowed a simple classical space-time interpretation at least in the static gauge adopted in the present formulation of D-branes.