Non-relativistic string monodromies

Spectral curve methods proved to be powerful techniques in the context of relativistic integrable string theories, since they allow us to derive the semiclassical spectrum from the minimal knowledge of a Lax pair and a classical string solution. In this paper we initiate the study of the spectral curve for non-relativistic strings in AdS(5) x S-5. First, we show that for string solutions whose Lax connection is independent of sigma, the eigenvalues of the monodromy matrix do not have any spectral parameter dependence. We remark that this particular behaviour also appears for relativistic strings in flat space. Second, for some simple non-relativistic string solutions where the path ordered exponential of the Lax connection can be computed, we show that the monodromy matrix is either diagonalisable with quasi-momenta independent of the spectral parameter, or non-diagonalisable. For the latter case, we propose a notion of generalised quasi-momenta, based on maximal abelian subalgebras, which retain a dependence on the spectral parameter.

Automated summary

In this paper, the authors study the spectral curve for non-relativistic strings in AdS(5) x S-5. They found that when the Lax connection of the string solution is independent of sigma, the eigenvalues of the monodromy matrix do not depend on the spectral parameter. For some simple non-relativistic string solutions, they show that the monodromy matrix can either be diagonalizable with quasi-momenta independent of the spectral parameter, or non-diagonalizable. In the latter case, they propose a notion of generalized quasi-momenta based on maximal abelian subalgebras which do depend on the spectral parameter.