A Worldsheet Derivation of the Classical Off-shell Boundary Action for the Dilaton in Half-Space

TL;DR

This paper derives the classical off-shell boundary action for the dilaton in a half-space using worldsheet methods, ensuring a well-defined variational principle and extending understanding of string theory in boundary conditions.

Contribution

It provides a worldsheet derivation of the off-shell boundary action for the dilaton in half-space, incorporating boundary conditions and leading order corrections in alpha prime.

Findings

Derived the sphere partition function for the dilaton with Neumann boundary conditions.

Obtained the total off-shell classical bosonic string action satisfying variational principles.

Extended the sphere prescription to include boundary effects in string theory.

Abstract

We use the method of images to present a worldsheet derivation of the sphere partition function for the dilaton in half-space to leading order in $\apr$ with Neumann boundary conditions. We use Tseytlin's sphere prescription to obtain the total (bulk and boundary) off-shell classical bosonic string action for the dilaton in half-space and show that it satisfies the requirement for a well-defined variational principle