Quantum corrections to $AdS_5 \times S^5$ left-invariant superstring current algebra

TL;DR

This paper uses the pure spinor formulation to compute quantum one-loop corrections to the superstring current algebra in the $AdS_5 imes S^5$ background, revealing corrections to simple poles affecting four-point amplitudes.

Contribution

It provides the first calculation of one-loop quantum corrections to the simple poles of the superstring current algebra in the $AdS_5 imes S^5$ background using pure spinor methods.

Findings

Simple poles receive quantum corrections from pure spinor Lorentz currents.

Double poles remain unaffected by quantum corrections.

Corrections to simple poles influence four-point amplitude calculations.

Abstract

In this work the pure spinor formulation of the superstring is used to study quantum corrections to the left current OPE algebra of the coset $PSU(2, 2|4)/SO(4, 1) \times SO(5)$ sigma model, which describes the superstring dynamics in the $AdS_5 \times S^5$ background. In particular, the one loop corrections to the simple poles of the bosonic currents are computed. Unlike the case of the double poles, we show that the simple poles suffer corrections, which are important since the simple poles contribute to the four point amplitudes. We show that the only contribution to the simple poles comes from the pure spinor Lorentz currents.