On the Problems with Background Independence in String Theory

TL;DR

This paper examines the challenges of background independence in string theory, specifically analyzing open string theory through conformal perturbation theory and proposing a conjecture for the all-order action.

Contribution

It provides a detailed calculation of the string field theory action to second order and introduces a conjecture for its form at all orders, addressing background independence issues.

Findings

Proper treatment of contact terms yields nontrivial equations of motion.

Calculated the string field theory action to second order.

Proposed a conjecture for the all-order form of the action.

Abstract

The problems with background independence are discussed in the example of open string theory. Based on the recent proposal by Witten I calculate the String Field Theory action in conformal perturbation theory to second order and demonstrate that the proper treatment of contact terms leads to nontrivial equations of motion. I conjecture the form of the field theory action to all orders.