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...:0905.0665[hep-th]. We verify that the regularized area of the world-sheets are consistent with expectations. ar X iv :1 10 4. 37 46 v2s[ he pth]s4sA ugs20 11 1 Introduction The Maldacena-Wilson loop =-=[1, 2]-=- has proven to be of pervasive usefulness as an observable in the AdS/CFT correspondence in particular [3], and in the gauge-gravity duality in general. Examples of areas of application include AdS/QC...

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...:0905.0665[hep-th]. We verify that the regularized area of the world-sheets are consistent with expectations. ar X iv :1 10 4. 37 46 v2s[ he pth]s4sA ugs20 11 1 Introduction The Maldacena-Wilson loop =-=[1, 2]-=- has proven to be of pervasive usefulness as an observable in the AdS/CFT correspondence in particular [3], and in the gauge-gravity duality in general. Examples of areas of application include AdS/QC...

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...ill show in the next section. The new solutions presented in section 4 are obtained by dressing the vacuum twice, i.e. by dressing the longitude solution. 3 Dressing method We use the dressing method =-=[48]-=- for the SU(2) sigma model to construct strings that live in S3 and have Euclidean worldsheet. Let ξA be the spacetime components of the string. We consider the element g = ( ξ1 + iξ2 −i(ξ3 + iξ4) −i(...

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...nst.} whose dynamics are captured by 1For R of rank O(N) the string is replaced by D3 and D5-branes [9–14], for R of rank O(N2) the AdS5 × S5 background geometry is replaced by a back-reacted version =-=[15, 16]-=-. 2The area is divergent and must be regularized by removing a term proportional to the Wilson loop’s perimeter. 3For recent progress concerning Wilson loops with constant scalar coupling, see [18]. 1...

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...de selection of parameters using numerical integration and have verified it with 10−6 percent-error accuracy. In figure 5 we show the results of numerical integration performed using the Cuba package =-=[53]-=- for a range of values of C, and for each range three representative values of b: √ 1 + C2 and √ 1 + C2 ± 3C/5. In the plot on the left the boxes are the predicted value from the RHS of (39) while the...

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... the Zarembo loops at strong coupling in [47]. In particular, the problem of finding classical string solutions of minimal area which end on the 1/8-BPS contours can be reduced to a sigma-model on S3 =-=[46]-=-. The procedure is non-trivial however, and not every solution of the sigma-model provides a Wilson loop. Indeed, there were originally only two solutions known, and these were obtained without recour...

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... ar X iv :1 10 4. 37 46 v2s[ he pth]s4sA ugs20 11 1 Introduction The Maldacena-Wilson loop [1, 2] has proven to be of pervasive usefulness as an observable in the AdS/CFT correspondence in particular =-=[3]-=-, and in the gauge-gravity duality in general. Examples of areas of application include AdS/QCD [4], scattering amplitudes [5], and Dp-brane theories [6–8]. In Euclidean N = 4 supersymmetric Yang-Mill...

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...15, 16]. 2The area is divergent and must be regularized by removing a term proportional to the Wilson loop’s perimeter. 3For recent progress concerning Wilson loops with constant scalar coupling, see =-=[18]-=-. 1 a Hermitian matrix model [33–35], exact for all values of N and λ. Recently, these two examples of Wilson loops were shown to arise from a larger class of generically 1/16-BPS Wilson loops with xµ...

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...e usefulness as an observable in the AdS/CFT correspondence in particular [3], and in the gauge-gravity duality in general. Examples of areas of application include AdS/QCD [4], scattering amplitudes =-=[5]-=-, and Dp-brane theories [6–8]. In Euclidean N = 4 supersymmetric Yang-Mills theory in four dimensions, this non-local, gauge-invariant operator couples both to the gauge field Aµ(x) and to the six rea...

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... open strings , ΘI(τ) provides a similar boundary condition on S5. At large N and λ = g2YMN , and for R of rank 1 O(1), the string worldsheet is classical and describes a minimal surface in AdS5 × S5 =-=[17]-=-. The area2 of this minimal surface is related to the logarithm of the expectation value of the Wilson loop 〈WR(C)〉. In this way we have replaced the problem of the strong coupling behaviour of WR(C) ...

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...nst.} whose dynamics are captured by 1For R of rank O(N) the string is replaced by D3 and D5-branes [9–14], for R of rank O(N2) the AdS5 × S5 background geometry is replaced by a back-reacted version =-=[15, 16]-=-. 2The area is divergent and must be regularized by removing a term proportional to the Wilson loop’s perimeter. 3For recent progress concerning Wilson loops with constant scalar coupling, see [18]. 1...

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...WR(C)〉 may be calculated via semi-classical fluctuation determinants [19–28]. The simplest Wilson loops (1) have ΘI(τ) = M Iµ ẋµ(τ) |ẋ(τ)| , M I µM I ν = δµν , (2) and were discovered by Zarembo in =-=[29]-=-. If the curve xµ(τ) lies in Rn, these Wilson loops are (1/2)n-BPS. They have trivial expectation value 〈W 〉 = 1, to all orders of perturbation theory [30–32]. The next-to-simplest Wilson loop (1) is ...

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...) = g and the coset constraint Ψ(λ̄)†Ψ(λ) = I. We find Ψ(λ) = ( ie−if(λ) 0 0 −ieif(λ) ) , f(λ) = λσ + τ 1 + λ2 . (25) The general N -soliton solution for the SU(n) sigma model has been constructed in =-=[49]-=- (see also [50–52]). Here we are interested in the special case n = 2 and we are focusing only on 1- and 2-soliton solutions, which can be expressed respectively as g1 = √ λ1 λ̄1 (α11I2×2 + h1h † 1)g0...

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...e longitude solution. We conclude in section 5 with a discussion. 4An original disagreement for Wilson loop correlators presented in [41] has since been retracted; the numerical analysis presented in =-=[43]-=- supports the two-dimensional Yang-Mills conjecture. 5Lmn is the Laguerre polynomial L m n (x) = 1/n! exp[x]x −m(d/dx)n(exp[−x]xn+m). 2 2 Pseudo-holomorphicity equations and sigma-model on S3 The 1/8-...