Boundary matching of D1–D5–P entropy to radial flow

Establish that the D1–D5 conformal field theory entropy is assigned to the integrated radial D1 flow of one complete boundary factor, thereby validating the boundary-matching conjecture and fixing the entropy-flow coefficient for a prescribed coarse-graining into source tubes.

Background

The paper relates the microscopic entropy of the D1–D5 conformal field theory, given by the standard three-charge expression, to the integrated radial D1 flow in the D1–D5–P supergravity frame. The proposed identification is not established in the present work; it is explicitly described as a boundary-matching conjecture. For a fixed coarse-graining into $\mathcal{N}$ source tubes, the conjecture determines the coefficient relating the CFT entropy to the flow.

The paper then observes that, conditional on this conjectural identification and the chosen tube normalization, T-duality transports the coefficient unchanged to the wrapped-D2 tubes in the D0–D4–F1 frame. Thus, proving the boundary matching would provide a microscopic justification for the capacity assigned to the T-dual wrapped-brane flow.