Non-relativistic string monodromies

Abstract

Spectral curve methods proved to be powerful techniques in the context of relativistic integrable string theories, since they allow 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${}_5\times S^5$. 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.

20 pages

References in corpus (17)

• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• Aspects of Nonrelativistic Strings
• The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
• Torsional string Newton-Cartan geometry for non-relativistic strings
• Quantum Wrapped Giant Magnon
• Constructing the AdS/CFT dressing factor
• On the Non-Relativistic Expansion of Closed Bosonic Strings
• Non-Riemannian isometries from double field theory
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Classical string solutions in Non-Relativistic AdS${}_5\times$S${}^5$: Closed and Twisted sectors
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Semiclassical spectrum for BMN string in $Sc{h}_5\times S^5$
• Coset space actions for nonrelativistic strings
• Extending the non-relativistic string AdS coset
• Newton-Cartan $D0$ branes from $D1$ branes and integrability

Cited by in corpus (6)

• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Light-Cone Gauge in Non-Relativistic AdS${}_5\times$S${}^5$ String Theory
• Non-Relativistic Holography from AdS${}_5$/CFT${}_4$
• Constructing Non-Relativistic AdS${}_5$/CFT${}_4$ Holography
• A perturbative approach to the non-relativistic string spectrum
• An integrable deformed Landau-Lifshitz model with particle production?