8,314 research outputs found

    Spinning strings in the η\eta-deformed Neumann-Rosochatius system

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    The sigma-model of closed strings spinning in the η\eta-deformation of AdS5×S5AdS_{5} \times S^{5} leads to an integrable deformation of the one-dimensional Neumann-Rosochatius mechanical system. In this article we construct general solutions to this system that can be written in terms of elliptic functions. The solutions correspond to closed strings with non-constant radii rotating with two different angular momenta in an η\eta-deformed three-sphere. We analyse the reduction of the elliptic solutions for some limiting values of the deformation parameter. For the case of solutions with constant radii we find the dependence of the classical energy of the string on the angular momenta as an expansion in the 't Hooft coupling.Comment: 17 pages. Latex. v2: Additional references. v3: Minor changes and updated reference

    Holographic correlation functions of hexagon Wilson loops with one local operator

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    We consider the ratio of the correlation function of an hexagon light-like Wilson loop with one local operator over the expectation value of the Wilson loop within the strong-coupling regime of the AdS/CFT correspondence. We choose the hexagon Wilson loop within a class of minimal solutions obtained by cutting and gluing light-like quadrangle loops. These surfaces do not have an interpretation in terms of dual scattering amplitudes but they still exhibit general features of the mixed correlation function. In the case of a regular null hexagon conformal symmetry constrains the space-time dependence of the correlator up to a function of three conformal cross-ratios. We obtain the leading-order contribution to the correlation function in the semiclassical approximation of large string tension, and express the result in terms of three conformal ratios in the case where the local operator is taken to be the dilaton. We include the analysis of an irregular Wilson loop obtained after a boost of the regular hexagon.Comment: 12 pages. Latex. v2: Reference added. v3: Added clarifications, published versio

    Elliptic solutions in the Neumann-Rosochatius system with mixed flux

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    Closed strings spinning in AdS_3 x S^3 x T^4 with mixed R-R and NS-NS three-form fluxes are described by a deformation of the one-dimensional Neumann-Rosochatius integrable system. In this article we find general solutions to this system that can be expressed in terms of elliptic functions. We consider closed strings rotating either in S^3 with two different angular momenta or in AdS_3 with one spin. In order to find the solutions we will need to extend the Uhlenbeck integrals of motion of the Neumann-Rosochatius system to include the contribution from the flux. In the limit of pure NS-NS flux, where the problem can be described by a supersymmetric WZW model, we find exact expressions for the classical energy in terms of the spin and the angular momenta of the spinning string.Comment: 18 pages. Latex. v2: Extended discussions, corrected misprints and added reference. Published versio

    Spinning strings in AdS_3 x S^3 with NS-NS flux

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    The sigma model describing closed strings rotating in AdS_3 x S^3 is known to reduce to the one-dimensional Neumann-Rosochatius integrable system. In this article we show that closed spinning strings in AdS_3 x S^3 x T^4 in the presence of NS-NS three-form flux can be described by an extension of the Neumann-Rosochatius system. We consider closed strings rotating with one spin in AdS_3 and two different angular momenta in S^3. For a class of solutions with constant radii we find the dependence of the classical energy on the spin and the angular momenta as an expansion in the square of the 't Hooft coupling of the theory.Comment: 14 pages. Latex. v2: Equations (3.19) and (3.28) corrected and reference added. v3: Expanded discussion on the WZW limit and additional references. Published version. v4: Misprints correcte

    Pulsating strings with mixed three-form flux

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    Circular strings pulsating in AdS3×S3×T4AdS_3 \times S^3 \times T^4 with mixed R-R and NS-NS three-form fluxes can be described by an integrable deformation of the one-dimensional Neumann-Rosochatius mechanical model. In this article we find a general class of pulsating solutions to this integrable system that can be expressed in terms of elliptic functions. In the limit of strings moving in AdS3AdS_{3} with pure NS-NS three-form flux, where the action reduces to the SL(2,R)SL(2,\mathbb{R}) WZW model, we find agreement with the analysis of the classical solutions of the system performed using spectral flow by Maldacena and Ooguri. We use our elliptic solutions in AdS3AdS_{3} to extend the dispersion relation beyond the limit of pure NS-NS flux.Comment: 10 pages. Late

    Minimal surfaces with mixed three-form flux

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    We study minimal area world sheets ending on two concentric circumferences on the boundary of Euclidean AdS3AdS_{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.Comment: 15 pages. Latex. v2: Title changed together with minor updates to emphasize that minimal area surfaces in the presence of mixed fluxes are found. v3: Published versio

    The SU(2)SU(2) Wess-Zumino-Witten spin chain sigma model

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    Classical strings propagating in AdS3×S3×T4AdS_{3}\times S^{3}\times T^{4} supported with Neveu-Schwarz-Neveu-Schwarz flux are described by a Wess-Zumino-Witten model. In this note, we study the emergence of their semiclassical SU(2)SU(2) spectrally flowed sectors as the Landau-Lifshitz limit of the underlying quantum spin chain. We consider the propagator in the coherent state picture, and find that the time interval is discretized proportionally to the lattice spacing. In the Landau-Lifshitz limit, where both time and space become continuous, we derive a path integral representation of the propagator for each spectrally flowed sector. We prove that the arbitrariness of the global phase of coherent states is mapped to the gauge freedom of the BB-field in the classical action. We show that higher order corrections in the Landau-Lifshitz limit are suppressed by inverse powers of the 't Hooft coupling.Comment: 10 pages, Latex. v2: Published version. v3: Acknowledgement adde
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