Yangian Symmetry of String Theory on $AdS_3 \times S^3 \times S^3 \times S^1$ with Mixed 3-form Flux

TL;DR

This paper uncovers the Yangian symmetry structure in the integrable superstring theory on a specific $AdS_3$ background with mixed flux, revealing its algebraic properties and classical r-matrix in the large tension limit.

Contribution

It provides the first explicit formulation of the Yangian symmetry for superstrings on $AdS_3 imes S^3 imes S^3 imes S^1$ with mixed flux, including RTT and evaluation representations.

Findings

Yangian symmetry is identified for the superstring background.

The algebraic relations are formulated via RTT realisation.

A universal classical r-matrix is derived in the large tension limit.

Abstract

We find the Yangian symmetry underlying the integrability of type IIB superstrings on $AdS_3 \times S^3 \times S^3 \times S^1$ with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux. The abstract commutation relations of the Yangian are formulated via RTT realisation, while its matrix realisation is in an evaluation representation depending on the quantised coefficient of the Wess-Zumino term. The construction naturally encodes a secret symmetry of the worldsheet scattering matrix whose generators map different Yangian levels to each other. We show that in the large effective string tension limit the Yangian becomes a deformation of a unitary loop algebra and we derive its universal classical r-matrix.