A Canonical Approach to Self-Duality of Dirichlet $3$-Brane

TL;DR

This paper demonstrates the self-duality of the Dirichlet 3-brane action under SL(2,R) duality in type IIB superstring theory using a canonical Hamiltonian approach, highlighting a method to replace gauge fields with their duals.

Contribution

It provides a canonical Hamiltonian framework to explicitly show the self-duality of the D3-brane action under SL(2,R) transformations, using direct phase space integration.

Findings

Self-duality of D3-brane action under SL(2,R) shown in Hamiltonian form

Boundary gauge field can be replaced by its dual through phase space integration

Method clarifies the canonical structure of D3-brane duality transformations

Abstract

The self-duality of Dirichlet $3$-brane action under the $SL(2,R)$ duality transformation of type IIB superstring theory is shown in the Hamiltonian form of the path integral for the partition function by performing the direct integration with respect to the boundary gauge field. Through the integration in the phase space the canonical momentum conjugate to the boundary gauge field can be effectively replaced by the dual gauge field.