Quantum Current Algebra for the $AdS_5 \times S^5$ Superstring

TL;DR

This paper computes one-loop corrections to operator product expansions in the pure spinor superstring sigma model on $AdS_5 imes S^5$, advancing understanding of quantum current algebra in this background.

Contribution

It provides the first explicit one-loop calculations of OPEs for currents in the pure spinor superstring on $AdS_5 imes S^5$, including their interactions with the energy-momentum tensor.

Findings

One-loop corrections to current-current OPEs are obtained.

OPEs between currents and the energy-momentum tensor are computed at tree level and one loop.

Results enhance the understanding of quantum aspects of the superstring in $AdS_5 imes S^5$.

Abstract

The sigma model describing the dynamics of the superstring in the $AdS_5 \times S^5$ background can be constructed using the coset $PSU(2,2|4)/SO(4,1)\times SO(5)$. A basic set of operators in this two dimensional conformal field theory is composed by the left invariant currents. Since these currents are not (anti) holomorphic, their OPE's is not determined by symmetry principles and its computation should be performed perturbatively. Using the pure spinor sigma model for this background, we compute the one-loop correction to these OPE's. We also compute the OPE's of the left invariant currents with the energy momentum tensor at tree level and one loop.