Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings

TL;DR

This paper introduces a two-parameter q-deformation of superstring models on AdS_3 x S^3 x M^4, demonstrating classical integrability, deformed symmetries, and consistent dispersion relations relevant for string theory.

Contribution

It constructs a novel two-parameter q-deformation of supercoset actions with integrability and symmetry properties, extending previous models to more general deformations.

Findings

The deformed models are classically integrable.

Deformed symmetry algebra is q-deformed, U_q_L(G) x U_q_R(G).

Near-BMN limit matches previous dispersion relations.

Abstract

We construct a two-parameter deformation of the Metsaev-Tseytlin action for supercosets with isometry group of the form G x G. The resulting action is classically integrable and is Poisson-Lie symmetric suggesting that the symmetry of the model is q-deformed, U_q_L(G) x U_q_R(G). Focusing on the cases relevant for strings moving in AdS_3 x S^3 x T^4 and AdS_3 x S^3 x S^3 x S^1, we analyze the corresponding deformations of the AdS_3 and S^3 metrics. We also construct a two-parameter $q$-deformation of the u(1) + psu(1|1)^2 x u(1) x R^3-invariant R-matrix and closure condition, which underlie the light-cone gauge S-matrix and dispersion relation of the aforementioned string theories. With the appropriate identification of parameters, the near-BMN limit of the dispersion relation is shown to agree with that found from the deformed supercoset sigma model.