The algebra of flat currents for the string on AdS_5 x S^5 in the light-cone gauge

TL;DR

This paper computes the algebra of flat currents for the string in AdS_5 x S^5 in light-cone gauge, revealing a closed form with non-ultralocal terms influenced by the radial coordinate, which suggests unambiguous transition matrix algebra.

Contribution

It extends previous work by explicitly calculating the algebra of flat currents in the AdS_5 x S^5 background with fixed kappa-symmetry, showing a closed algebra with specific non-ultralocal terms.

Findings

The algebra of flat currents has a closed form.

Non-ultralocal terms are weighted by e^{} depending on the radial coordinate.

The transition matrix algebra is likely unambiguous.

Abstract

We continue the program initiated in hep-th/0411200 and calculate the algebra of the flat currents for the string on AdS_5 x S^5 background in the light-cone gauge with kappa-symmetry fixed. We find that the algebra has a closed form and that the non-ultralocal terms come with a weight factor e^{\phi} that depends on the radial AdS_5 coordinate. Based on results in two-dimensional sigma models coupled to gravity via the dilaton field, this suggests that the algebra of transition matrices in the present case is likely to be unambigous.