Dual D-Brane Actions

TL;DR

The paper develops dual Dp-brane actions by dualizing the world-volume $U(1)$ gauge field, producing a dual $p-2$-form on the brane. It verifies the expected duality properties: D1 and D3 transform in line with type IIB $SL(2,\mathbb{Z})$, while D2 and D4 map consistently with the type IIA–11D M-theory connection, with the D4 dual matching the M5-brane’s double-dimensional reduction. Gauge-fixed analyses corroborate these dualities in static gauges, and the work extends to backgrounds with constant dilaton and axion, revealing the classical $SL(2,\mathbb{R})$ structure (quantumly reduced to $SL(2,\mathbb{Z})$). The study delineates the limitations for higher $p$ and lays groundwork for future extensions to nontrivial backgrounds and higher-dimensional branes.

Abstract

Dual super Dp-brane actions are constructed by carrying out a duality transformation of the world-volume U(1) gauge field. The resulting world-volume actions, which contain a (p - 2)-form gauge field, are shown to have the expected properties. Specifically, the D1-brane and D3-brane transform in ways that can be understood on the basis of the SL(2, Z) duality of type IIB superstring theory. Also, the D2-brane and the D4-brane transform in ways that are expected on the basis of the relationship between type IIA superstring theory and 11d M theory. For example, the dual D4-brane action is shown to coincide with the double-dimensional reduction of the recently constructed M5-brane action. The implications for gauge-fixed D-brane actions are discussed briefly.