Integrable Lambda Models And Chern-Simons Theories

Understand

In this note we reveal a connection between the phase space of lambda models on $S^{1}\times \mathbb{R}$ and the phase space of double Chern-Simons theories on $D\times \mathbb{R}$ and explain in the process the origin of the non-ultralocality of the Maillet bracket, which emerges as a boundary algebra.

• In particular, this means that the (classical) $AdS_{5}\times S^{5}$ lambda model can be understood as a double Chern-Simons theory defined on the Lie superalgebra $\mathfrak{psu}(2,2|4)$ after a proper dependence of the spectral parameter is introduced.
• This offers a possibility for avoiding the use of the problematic non-ultralocal Poisson algebras that preclude the introduction of lattice regularizations and the application of the QISM to string sigma models.
• The utility of the equivalence at the quantum level is, however, still to be explored.