Yangian Symmetry of String Theory on $Ad{S}_3\times S^3\times S^3\times S^1$ with Mixed 3-form Flux

Abstract

We find the Yangian symmetry underlying the integrability of type IIB superstrings on $Ad{S}_3\times S^3\times S^3\times S^1$ 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.

24 pages; added references

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• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• Boost generator in AdS_3 integrable superstrings for general braiding
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• A study of integrable form factors in massless relativistic AdS_3
• On N-spike strings in conformal gauge with NS-NS fluxes
• Minimal surfaces with mixed three-form flux
• Neumann-Rosochatius system for (m,n) string in $Ad{S}_3\times S^3$ with mixed flux
• Geometry of Massless Scattering in Integrable Superstring
• $N$-spike string in $Ad{S}_3\times S^1$ with mixed flux
• Fermion zero modes for the mixed-flux AdS${}_3$ giant magnon
• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory
• Norms and scalar products for AdS_3
• Neumann-Rosochatius system for rotating strings in $Ad{S}_3\times S^3\times S^3\times S^1$ with flux
• On finite-size spiky strings in $Ad{S}_3\times S^3\times T^4$ with mixed fluxes