Action for (Free) Open String Modes in AdS Space Using the Loop Variable Approach

TL;DR

This paper extends the loop variable approach to derive gauge-invariant equations of motion for open string modes in AdS space, resolving ambiguities present in curved backgrounds and obtaining the full action in special cases.

Contribution

It adapts the loop variable method to AdS backgrounds, providing a way to determine the complete action for open string modes in these curved spacetimes.

Findings

Exact action for open string modes in AdS space derived.

Method resolves ambiguities related to curvature couplings.

Demonstrates the approach for massive spin 2 fields.

Abstract

The loop variable technique (for open strings in flat space) is a gauge invariant generalization of the renormalization group method for obtaining equations of motion. Unlike the beta functions, which are only proportional to the equations of motion, here it gives the full equation of motion. In an earlier paper, a technique was described for adapting this method to open strings in gravitational backgrounds. However unlike the flat space case, these equations cannot be derived from an action and are therefore not complete. This is because there are ambiguities in the method that involve curvature couplings that cannot be fixed by appealing to gauge invariance alone but need a more complete treatment of the closed string background. An indirect method to resolve these ambiguities is to require symmetricity of the second derivatives of the action. In general this will involve modifying the equations by terms with arbitrarily high powers of curvature tensors. This is illustrated for the massive spin 2 field. It is shown that in the special case of an AdS or dS background, the exact action can easily be determined in this way.