Generalized Conformal Symmetry in D-Brane Matrix Models

TL;DR

The paper extends generalized conformal symmetry (GCS) to D$p$-brane systems by promoting the Yang-Mills coupling to a background field and deriving field-dependent special conformal transformations that match both the supergravity background and the SYM matrix model at one loop. It shows that quantum corrections on the YM side, implemented via a BRST-adjusted SCT, yield a modified transformation that reproduces AdS-like behavior after appropriate Higgs-field or coordinate redefinitions, establishing a robust YM–SUGRA correspondence for general p. The work also demonstrates how GCS constrains the DBI action for probe branes and discusses general multi-brane configurations where a simple space-time interpretation is lost, highlighting the need for a covariant formulation. These results support a deep link between bulk supergravity dynamics and loop-corrected YM dynamics, with potential implications for higher-loop non-renormalization theorems and bulk–boundary holography beyond conventional AdS/CFT settings.

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.