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 work addresses κ-symmetry fixing for strings and branes on $AdS_{5}\times S^{5}$ by classifying constant projectors via their Dirac conjugation and charge-conjugation properties. It shows that Type $S$ projectors yield supervielbeins with fermion dependence at most quadratic, enabling a tractable κ-fixed gauge, while Type $L$ projectors lead to prohibitively high fermionic orders and are set aside. Focusing on Type IIB on $AdS_{5}\times S^{5}$, the authors construct a lightcone-like κ-gauge (e.g., $P=\frac{1}{\sqrt{2}}\gamma^{0}\gamma^{+}$) and derive the corresponding GS action, demonstrating its reduction to the standard flat-space lightcone action in the limit $e\to 0$ with appropriate rescalings. The framework clarifies which physical states can be described within a given κ-fixed gauge and paves the way for a controlled large-radius (AdS) expansion of the string dynamics.

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.