On the Dynamics of finite-gap solutions in classical string theory

Dorey, Nick; Vicedo, Benoit

doi:10.1088/1126-6708/2006/07/014

Cited by 81 publications

(219 citation statements)

References 25 publications

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“…This is the main idea of the Pohlmeyer reduction [59] which we rederive here as it applies to our particular problem. Similar considerations in the context of string theory are well-known, for example see [32][33][34][35][36][37][38][39][40][41][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57] and [60].…”

Section: Jhep11(2014)065mentioning

confidence: 81%

“…To find solutions in all those cases it is important to exploit the integrability properties of the equations of motion which are the same as those of the closed string. Recently, in the case of closed, Euclidean, plane Wilson loops (with constant scalar) an infinite parameter family of analytical solutions was found using Riemann theta functions [28,29] following results from the mathematical literature [30,31] and from previous results for closed strings [32][33][34][35][36][37][38][39][40][41]. This integrability construction for the Wilson loop was further discussed in [42] and also in [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57].…”

Section: Jhep11(2014)065mentioning

confidence: 99%

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Wilson loops and minimal area surfaces in hyperbolic space

Kruczenski

2014

J. High Energ. Phys.

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The AdS/CFT correspondence relates Wilson loops in N = 4 SYM theory to minimal area surfaces in AdS space. If the loop is a plane curve the minimal surface lives in hyperbolic space H 3 (or equivalently Euclidean AdS 3 space). We argue that finding the area of such extremal surface can be easily done if we solve the following problem: given two real periodic functions V 0,1 (s), V 0,1 (s + 2π) = V 0,1 (s) a third periodic function V 2 (s) is to be found such that all solutions to the equation −∂ 2] for any value of λ. This problem is equivalent to the statement that the monodromy matrix is trivial. It can be restated as that of finding a one complex parameter family of curves X(λ, s) where X(λ = 1, s) is the given shape of the Wilson loop and such that the Schwarzian derivative {X(λ, s), s} is meromorphic in λ with only two simple poles. We present a formula for the area in terms of the functions V 0,1,2 and discuss solutions to these equivalent problems in terms of theta functions. Finally, we also consider the near circular Wilson loop clarifying its integrability properties and rederiving its area using the methods described in this paper.

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Section: Jhep11(2014)065mentioning

confidence: 81%

Section: Jhep11(2014)065mentioning

confidence: 99%

Wilson loops and minimal area surfaces in hyperbolic space

Kruczenski

2014

J. High Energ. Phys.

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“…For the AdS 5 × S 5 [16,17,[63][64][65][66][67][68] and AdS 4 × CP 3 [21] backgrounds the finite-gap method yields a set of coupled integral equations, which on the one hand parameterize possible classical solutions of the sigmamodel and on the other hand can be regarded as the classical limit of the Bethe equations for the quantum spectrum of the string. We first describe the general scheme of finite-gap integration, as applied to the 4 cosets, and then specify the general construction to the case at hand, the sigma model on AdS 3 × S 3 × S 3 × S 1 .…”

Section: Jhep03(2010)058mentioning

confidence: 99%

Integrability and the AdS 3/CFT 2 correspondence

Babichenko

Stefański

Zarembo

2010

J. High Energ. Phys.

188

360

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Abstract:We investigate the AdS 3 /CFT 2 correspondence for theories with 16 supercharges using the integrability approach. We construct Green-Schwarz actions for Type IIB strings on AdS 3 × S 3 × M 4 where M 4 = T 4 or S 3 × S 1 using the coset approach. These actions are based on a Z 4 automorphism of the super-coset D(2, 1; α)×D(2, 1; α)/SO(1, 2)× SO(3) × SO(3). The equations of motion admit a representation in terms of a Lax connection, showing that the system is classically integrable. We present the finite gap equations for these actions. When α = 0 , 1/2 , 1 we propose a set of quantum Bethe equations valid at all values of the coupling. The AdS 3 /CFT 2 duals contain novel massless modes whose role remains to be explored.

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“…We can define the current 14) which is invariant under the global symmetry and, under the local symmetry transform as…”

Section: Equations Of Motionmentioning

confidence: 99%

Notes on Euclidean Wilson loops and Riemann theta functions

2012

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The AdS/CFT correspondence relates Wilson loops in N = 4 SYM theory to minimal area surfaces in AdS 5 space. In this paper we consider the case of Euclidean flat Wilson loops which are related to minimal area surfaces in Euclidean AdS 3 space. Using known mathematical results for such minimal area surfaces we describe an infinite parameter family of analytic solutions for closed Wilson loops. The solutions are given in terms of Riemann theta functions and the validity of the equations of motion is proven based on the trisecant identity. The world-sheet has the topology of a disk and the renormalized area is written as a finite, one-dimensional contour integral over the world-sheet boundary. An example is discussed in detail with plots of the corresponding surfaces. Further, for each Wilson loops we explicitly construct a one parameter family of deformations that preserve the area. The parameter is the so called spectral parameter. *

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On the Dynamics of finite-gap solutions in classical string theory

Cited by 81 publications

References 25 publications

Wilson loops and minimal area surfaces in hyperbolic space

Wilson loops and minimal area surfaces in hyperbolic space

Integrability and the AdS 3/CFT 2 correspondence

Notes on Euclidean Wilson loops and Riemann theta functions

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