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It is well known that the $AdS_{5}\times S^{5}$ superstring equations of motion either in the Green-Schwarz (GS) or in the pure spinor (PS) formulation can be cast into a zero curvature equation satisfied by a Lax pair.
Recently significant progress has been made in deforming the $AdS_{5}\times S^{5}$ structure of the GS superstring while preserving the integrability and its local symmetries. The $\eta$-deformation describes a string moving in a generalized supergravity background, and its main ingredient is a linear operator which solves the modified classical Yang-Baxter equation.
In this work we present an integrable deformation of the $AdS_{5}\times S^{5}$ PS superstring based on homological perturbation theory. The resulting model describes a PS superstring in a $\eta$-background. Its equations of motion, Lax connection and BRST symmetry are discussed. We found that the $\eta$-deformation of the superstring is produced by the perturbative action of one state in the cohomology of $AdS_{5}\times S^{5}$.
| arXiv | https://arxiv.org/abs/1807.10432v1 |
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