ND Tadpoles as New String States and Quantum Mechanical Particle-Wave Duality from World-Sheet T-Duality

TL;DR

This paper explores new string objects called ND tadpoles, demonstrating how world-sheet T-duality induces quantum particle-wave duality and introduces a boundary operator that switches boundary conditions.

Contribution

It introduces ND tadpoles in bosonic open string theory and shows how world-sheet T-duality leads to quantum duality and a boundary operator for boundary condition changes.

Findings

ND tadpoles must exist due to s-t duality.

World-sheet T-duality induces quantum particle-wave duality.

A boundary operator 'Zipper' changes boundary conditions.

Abstract

We consider new objects in bosonic open string theory -- ND tadpoles, which have N(euman) boundary conditions at one end of the world-sheet and D(irichlet) at the other, must exist due to s-t duality in a string theory with both NN strings and D-branes. We demonstrate how to interpolate between N and D boundary conditions. In the case of mixed boundary conditions the action for a quantum particle is induced on the boundary. Quantum-mechanical particle-wave duality, a dual description of a quantum particle in either the coordinate or the momentum representation, is induced by world-sheet T-duality. The famous relation between compactification radii is equivalent to the quantization of the phase space area of a Planck cell. We also introduce a boundary operator - a ``Zipper'' which changes the boundary condition from N into D and vice versa.