SL(2, Z) invariant rotating (m, n) strings in $$AdS_3\times S^3$$ A d S 3 × S 3 with mixed flux

Circular strings pulsating in AdS 3 × S 3 × 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 AdS 3 with pure NS-NS three-form flux, where the action reduces to the SL(2, 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 AdS 3 to extend the dispersion relation beyond the limit of pure NS-NS flux.

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“…When we combine this expression with the Virasoro constraint (28) and solve for u 0 we conclude that…”

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confidence: 99%

Pulsating strings with mixed three-form flux

Hernández

Nieto

Ruiz

2018

J. High Energ. Phys.

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“…Moreover, both the elliptic modulus κ and the elliptic characteristic n vanish. Therefore, it is straightforward to show that the length of the interval T tends to 2 24) and the ratio R of the radii tends tō R = exp kπ…”

Section: Minimal Area Surfacesmentioning

confidence: 99%

Minimal surfaces with mixed three-form flux

2019

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We study minimal area world sheets ending on two concentric circumferences on the boundary of Euclidean AdS 3 with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three-form fluxes. We solve the problem by reducing the system to a one-dimensional integrable model. We find that the Neveu-Schwarz-Neveu-Schwarz flux term either brings the surface near to the boundary or separates the circumferences. In the limit of pure Neveu-Schwarz-Neveu-Schwarz 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 Neveu-Schwarz-Neveu-Schwarz flux the elliptic curve degenerates.

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Neumann–Rosochatius system for (m,n) string in $$AdS_3 \times S^3$$ with mixed flux

Chakraborty

Panigrahi

2021

Eur. Phys. J. C

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Abstract$$SL(2,{\mathbb {Z}})$$ S L ( 2 , Z ) invariant action for probe (m, n) string in $$AdS_3\times S^3\times T^4$$ A d S 3 × S 3 × T 4 with mixed three-form fluxes can be described by an integrable deformation of an one-dimensional Neumann–Rosochatius (NR) system. We present the deformed features of the integrable model and study general class of rotating and pulsating solutions by solving the integrable equations of motion. For the rotating string, the explicit solutions can be expressed in terms of elliptic functions. We make use of the integrals of motion to find out the scaling relation among conserved charges for the particular case of constant radii solutions. Then we study the closed (m, n) string pulsating in $$R_t\times S^3$$ R t × S 3 . We find the string profile and calculate the total energy of such pulsating string in terms of oscillation number $$({\mathcal {N}})$$ ( N ) and angular momentum $$({\mathcal {J}})$$ ( J ) .

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SL(2, Z) invariant rotating (m, n) strings in $$AdS_3\times S^3$$ A d S 3 × S 3 with mixed flux

Cited by 3 publications

References 32 publications

Pulsating strings with mixed three-form flux

Pulsating strings with mixed three-form flux

Minimal surfaces with mixed three-form flux

Neumann–Rosochatius system for (m,n) string in $$AdS_3 \times S^3$$ with mixed flux

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