On the Gauge Fixing of the k Symmetry on AdS and Flat Background: the Lightcone Action for the Type IIb String on AdS_{5} X S_{5}

TL;DR

This paper systematically classifies kappa symmetry fixings for superstrings and branes using constant projectors, deriving a lightcone gauge action for the Type IIB string on AdS5×S5 that simplifies to the flat-space lightcone Green-Schwarz action.

Contribution

It introduces a classification scheme for kappa symmetry fixings via constant projectors and derives a lightcone gauge action for the Type IIB superstring on AdS5×S5.

Findings

Classified kappa symmetry fixings based on Dirac conjugation properties.

Identified projectors leading to quadratic fermionic vielbeins.

Derived a lightcone gauge action that reduces to the flat-space GS string action.

Abstract

We explore all the possible ways of fixing the kappa symmetry for both branes and strings by means of a constant projector. We find that they can be classified according to their behaviour under Dirac conjugation and conjugation. This latter controls the maximum power of the fermionic variables in which the (super)vielbein can be expanded while the former determines which states cannot be described in the gauge. In particular there exists an interesting class of projectors for which vielbein are at most quadratic in the fermionic variables. As an example we compute the action for the type IIb on a AdS_{5} X S_{5} background with a lightcone-like projector; this action reduces to the usual lightcone GS string action in the flat limit.