The AdS_5 x S^5 superstrings in the generalized light-cone gauge

TL;DR

This paper analyzes the Hamiltonian structure of superstrings in AdS_5 x S^5 under a generalized light-cone gauge, revealing non-commutative transverse coordinates upon quantization.

Contribution

It provides a canonical Hamiltonian formulation of superstrings in AdS_5 x S^5 with a generalized light-cone gauge, including treatment of fermionic constraints via Dirac brackets.

Findings

Transverse coordinates become non-commutative after quantization.

All fermionic constraints are second class and handled with Dirac brackets.

The Hamiltonian dynamics are explicitly derived in the light-cone gauge.

Abstract

The kappa-symmetry-fixed Green-Schwarz action in the AdS_5 x S^5 background is treated canonically in a version of the light-cone gauge. After reviewing the generalized light-cone gauge for a bosonic sigma model, we present the Hamiltonian dynamics of the Green-Schwarz action by using the transverse degrees of freedom. The remaining fermionic constraints are all second class, which we treat by the Dirac bracket. Upon quantization, all of the transverse coordinates are inevitably non-commutative.