Background independence of effective actions at critical dimension

TL;DR

This paper explores the background independence of effective actions in string theory at the critical dimension, extending the concept to open manifolds and boundary conditions, supported by explicit calculations.

Contribution

It proposes that effective actions are independent of boundary character in open manifolds and confirms this through calculations at order α' in bosonic string theory.

Findings

Effective action at critical dimension is background independent for closed manifolds.

Boundary couplings for spacelike and timelike boundaries are identical at order α' in bosonic string theory.

Supports the hypothesis of boundary independence in open spacetime manifolds.

Abstract

Recently, by explicit calculations at orders $\alpha',\alpha'^2,\alpha'^3$, it has been observed that the effective action of string theory at the critical dimension is independent of the background for the closed spacetime manifolds. In this paper we speculate that for the open spacetime manifolds, the effective action is even independent of the character of the boundary, \ie the boundary couplings for timelike and spacelike boundaries are the same. We support this proposal by calculating the boundary couplings in the bosonic string theory at order $\alpha'$ for the spacelike boundary and show that they are the same as the couplings for the timelike boundary that have been recently found.