Bethe ansatz for quantum-deformed strings

Two distinct eta-deformations of strings on AdS(5)xS(5) can be defined; both amount to integrable quantum deformations of the string non-linear sigma model, but only one is itself a superstring background. In this paper we compare their conjectured all-loop worldsheet S matrices and derive the corresponding Bethe equations. We find that, while the S matrices are apparently different, they lead to the same Bethe equations. Moreover, in either case the eigenvalues of the transfer matrix, which encode the conserved charges of each system, also coincide. We conclude that the integrable structure underlying the two constructions is essentially the same. Finally, we write down the full Bethe-Yang equations describing the asymptotic spectrum of the superstring background.

Automated summary

In this paper, two distinct eta-deformations of strings on AdS(5)xS(5) were compared, with both leading to integrable quantum deformations of the string non-linear sigma model. While their S matrices are apparently different, they result in the same Bethe equations, indicating that the integrable structure underlying the two constructions is essentially the same. Additionally, the eigenvalues of the transfer matrix in each case coincide, further supporting the conclusion that the two constructions share a common integrable structure.