A Note on Classical Solution of Chaplygin-gas as D-brane

TL;DR

This paper explores classical solutions of bosonic d-branes by reducing the problem to the Chaplygin gas and minimal surface equations, revealing connections to the Plateau problem and Einstein equations.

Contribution

It introduces a novel approach linking d-brane solutions to minimal surfaces and the Plateau problem, providing explicit solutions and discussing their relation to Hamiltonian-BRST formalism.

Findings

Solutions derived from minimal surfaces in various dimensions.

Connection established between d-brane equations and Einstein vacuum equations.

Identification of the Plateau problem as a key aspect of d-brane classical solutions.

Abstract

The classical solution of bosonic d-brane in (d+1,1) space-time is studied. We work with light-cone gauge and reduce the problem into Chaplygin gas problem. The static equation is equivalent to vanishing of extrinsic mean curvature, which is similar to Einstein equation in vacuum. We show that the d-brane problem in this gauge is closely related to Plateau problem, and we give some non-trivial solutions from minimal surfaces. The solutions of d-1,d,d+1 spatial dimensions are obtained from d-dimensional minimal surfaces as solutions of Plateau problem. In addition we discuss on the relation to Hamiltonian-BRST formalism for d-branes.