Moduli dynamics of AdS<sub>3</sub>strings

Jevicki, Antal; Jin, Kewang

doi:10.1088/1126-6708/2009/06/064

Cited by 52 publications

(66 citation statements)

References 36 publications

(46 reference statements)

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“…This is the main idea of the Pohlmeyer reduction [17] 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 [18], [20], [11], [15].…”

Section: Equations Of Motionsupporting

confidence: 54%

“…In the context of Minkowski space-time this procedure was used by Jevicki and Jin [18] to find new spiky string [19] solutions and by Alday and Maldacena [11] to compute certain light-like Wilson loops. In the case of Euclidean AdS 3 that we are interested in here, we can use embedding coordinates X µ=0...3 parameterizing a space R 3,1 and subjected to the constraint…”

Section: Equations Of Motionmentioning

confidence: 99%

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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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Section: Equations Of Motionsupporting

confidence: 54%

Section: Equations Of Motionmentioning

confidence: 99%

Notes on Euclidean Wilson loops and Riemann theta functions

2012

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“…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%

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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“…In that work the minimal area surfaces were constructed analytically in terms of Riemann theta functions associated to hyperelliptic Riemman surfaces closely following previous work by M. Babich and A. Bobenko [15,16]. It also follows related work where Wilson loops were studied or theta functions were used in similar problems, for example in [17][18][19][20][21][22][23][24][25][26][27][28][29][34][35][36][37][38]. 1 Much of that work was motivated by the relation to scattering amplitudes [28,29] which we do not pursue here.…”

Section: Jhep05(2014)037mentioning

confidence: 99%

Wilson loops and Riemann theta functions II

Kruczenski

Ziama

2014

J. High Energ. Phys.

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In this paper we extend and simplify previous results regarding the computation of Euclidean Wilson loops in the context of the AdS/CFT correspondence, or, equivalently, the problem of finding minimal area surfaces in hyperbolic space (Euclidean AdS 3 ). If the Wilson loop is given by a boundary curve X(s) we define, using the integrable properties of the system, a family of curves X(λ, s) depending on a complex parameter λ known as the spectral parameter. This family has remarkable properties. As a function of λ, X(λ, s) has cuts and therefore is appropriately defined on a hyperelliptic Riemann surface, namely it determines the spectral curve of the problem. Moreover, X(λ, s) has an essential singularity at the origin λ = 0. The coefficients of the expansion of X(λ, s) around λ = 0, when appropriately integrated along the curve give the area of the corresponding minimal area surface.Furthermore we show that the same construction allows the computation of certain surfaces with one or more boundaries corresponding to Wilson loop correlators. We extend the area formula for that case and give some concrete examples. As the main example we consider a surface ending on two concentric circles and show how the boundary circles can be deformed by introducing extra cuts in the spectral curve.

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Moduli dynamics of AdS₃strings

Cited by 52 publications

References 36 publications

Notes on Euclidean Wilson loops and Riemann theta functions

Notes on Euclidean Wilson loops and Riemann theta functions

Wilson loops and minimal area surfaces in hyperbolic space

Wilson loops and Riemann theta functions II

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Moduli dynamics of AdS3strings

Cited by 52 publications

References 36 publications

Notes on Euclidean Wilson loops and Riemann theta functions

Notes on Euclidean Wilson loops and Riemann theta functions

Wilson loops and minimal area surfaces in hyperbolic space

Wilson loops and Riemann theta functions II

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Moduli dynamics of AdS₃strings