Background Independence, Gauge Invariance and Equations of Motion for Closed String Modes

TL;DR

This paper develops a method to derive background independent, gauge invariant, and generally covariant equations of motion for closed string modes, relaxing previous restrictions on the background metric.

Contribution

It introduces a new prescription for mapping loop variables to spacetime fields that ensures background independence and covariance for arbitrary backgrounds.

Findings

Equations are gauge invariant and generally covariant for arbitrary backgrounds.

Extra curvature-coupled terms are necessary for consistency.

Method applies to both open and closed string modes.

Abstract

In an earlier paper [arXiv:1408.0484] gauge invariant and background covariant equations for closed string modes were obtained from the exact renormalization group equation of the world sheet theory. The background metric (but not the physical metric) had to be flat and hence the method was not manifestly background independent. In this paper the restrictions on the background metric are relaxed. A simple prescription for the map from loop variables to space time fields is given whereby for arbitrary backgrounds the equations are generally covariant and gauge invariant. Extra terms involving couplings of the curvature tensor to (derivatives of) the Stueckelberg fields have to be added. The background metric is chosen to be the physical metric without any restrictions. This method thus gives manifestly background independent gauge invariant and general covariant equations of motion for both open and closed string modes.