Abstract:
We show that bosonic spinning strings on the $\eta$-deformed $\mathrm{(AdS_5\times S^5)}$ background are naturally described as periodic solutions of a novel finite-dimensional integrable system which can be viewed as a deformation of the celebrated Neumann model. For this deformed model we find the Lax representation and the analogue of the Uhlenbeck integrals.
G.A. acknowledges the support by the Netherlands Organization for Scientific Research (NWO) under the VICI grant 680-47-602. The work by G.A. is also a part of the ERC Advanced grant research programme No. 246974, “Supersymmetry: a window to nonperturbative physics” and of the D-ITP consortium, a program of the NWO that is funded
by the Dutch Ministry of Education, Culture and Science (OCW). The work of D.M. was supported in part by Compania Colombiana Automotriz S.A. and Fundacion Mazda para el Arte y la Ciencia.