Abstract
We study minimal area world sheets ending on two concentric circumferences on the boundary of Euclidean $AdS_{3}$ with mixed R-R and NS-NS three-form fluxes. We solve the problem by reducing the system to a one-dimensional integrable model. We find that the NS-NS flux term either brings the surface near to the boundary or separates the circumferences. In the limit of pure NS-NS flux the solution adheres to the boundary in the former case and the outer radius diverges in the latter. We further construct the underlying elliptic spectral curve, which allows us to analyze the deformation of other related minimal surfaces. We show that in the regime of pure NS-NS flux the elliptic curve degenerates.
Highlights
The AdS=CFT correspondence states that the strong coupling limit of the expectation value of Wilson loop observables can be described by classical string solutions
A general class of minimal surfaces was found in Ref. [2] using a periodic ansatz that allowed the authors to reduce the analysis of the nonlinear sigma model for the string to the construction of solutions to one-dimensional integrable systems
This periodic ansatz is closely related to the ansatz introduced in Ref. [3] to transform the analysis of the energy spectrum of circular strings spinning in AdS5 × S5 into the study of periodic solutions to the Neumann-Rosochatius integrable system, which is a model of oscillators on a sphere
Summary
The AdS=CFT correspondence states that the strong coupling limit of the expectation value of Wilson loop observables can be described by classical string solutions. [2] using a periodic ansatz that allowed the authors to reduce the analysis of the nonlinear sigma model for the string to the construction of solutions to one-dimensional integrable systems. This periodic ansatz is closely related to the ansatz introduced in Ref. [4], it was shown that the analysis of closed strings spinning in AdS3 × S3 × T4 with a mixture of RamondRamond (R-R) and Neveu-Schwarz-Neveu-Schwarz (NS-NS) three-form fluxes can be performed by means of an integrable deformation of the Neumann-Rosochatius mechanical system IV, we summarize our results and comment on some open issues and future perspectives
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