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16
Notes on Euclidean Wilson loops and Riemann Theta functions,” Phys
 Rev. D
"... The AdS/CFT correspondence relates Wilson loops inN = 4 SYM theory to minimal area surfaces in AdS5 space. In this paper we consider the case of Euclidean flat Wilson loops which are related to minimal area surfaces in Euclidean AdS3 space. Using known mathematical results for such minimal area su ..."
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The AdS/CFT correspondence relates Wilson loops inN = 4 SYM theory to minimal area surfaces in AdS5 space. In this paper we consider the case of Euclidean flat Wilson loops which are related to minimal area surfaces in Euclidean AdS3 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 worldsheet has the topology of a disk and the renormalized area is written as a finite, onedimensional contour integral over the worldsheet 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. Finally, for genus three we find a map between these Wilson loops and closed curves inside the Riemann surface.
Correlation function of circular Wilson loops at strong coupling
, 2013
"... We study the correlation function of two circular Wilson loops at strong coupling in N = 4 super YangMills theory. Using the AdS/CFT correspondence, the problem maps to finding the minimal surface between two circles defined on the boundary of AdS, and the fluctuations around the classical solution ..."
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We study the correlation function of two circular Wilson loops at strong coupling in N = 4 super YangMills theory. Using the AdS/CFT correspondence, the problem maps to finding the minimal surface between two circles defined on the boundary of AdS, and the fluctuations around the classical solution in AdS5×S5. At the classical level, we derive the string solution in H3×S1 explicitly, and focus on properties such as stability and phase transition. Furthermore, a computation of the associated algebraic curve is given. At the quantum level, the oneloop partition function is constructed by introducing quadratic bosonic and fermionic fluctuations around the classical solution, embedded in AdS5 × S5. We find an analytic, formal expression for the partition function in terms of an infinite product by employing the Gel’fandYaglom method and supersymmetric regularization. We regulate the expression and evaluate the partition function numerically.
Localization at Large N
"... We review how localization is used to probe holographic duality and, more generally, nonperturbative dynamics of fourdimensional N = 2 supersymmetric gauge theories in the planar largeN limit. 1 ..."
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We review how localization is used to probe holographic duality and, more generally, nonperturbative dynamics of fourdimensional N = 2 supersymmetric gauge theories in the planar largeN limit. 1
From weak to strong coupling in ABJM theory
, 2011
"... The partition function of N = 6 supersymmetric Chern–Simonsmatter theory (known as ABJM theory) on S3, as well as certain Wilson loop observables, are captured by a zero dimensional supermatrix model. This super–matrix model is closely related to a matrix model describing topological Chern–Simons ..."
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The partition function of N = 6 supersymmetric Chern–Simonsmatter theory (known as ABJM theory) on S3, as well as certain Wilson loop observables, are captured by a zero dimensional supermatrix model. This super–matrix model is closely related to a matrix model describing topological Chern–Simons theory on a lens space. We explore further these recent observations and extract more exact results in ABJM theory from the matrix model. In particular we calculate the planar free energy, which matches at strong coupling the classical IIA supergravity action on AdS4 ×CP3 and gives the correct N3/2 scaling for the number of degrees of freedom of the M2 brane theory. Furthermore we find contributions coming from worldsheet instanton corrections in CP3. We also calculate nonplanar corrections, both to the free energy and to the Wilson loop expectation values. This matrix model appears also in the study of topological strings on a toric Calabi–Yau manifold, and an intriguing connection arises between the space of couplings of the planar ABJM theory and the moduli space of this Calabi–Yau. In particular it suggests that, in addition to the usual perturbative and strong coupling (AdS) expansions, a third natural expansion locus is the line where one of the two ’t Hooft couplings vanishes and the other is finite. This is the conifold locus of the Calabi–Yau, and leads to an expansion around topological Chern–Simons theory. We present some explicit results for the partition function and Wilson loop observables around this locus.
Generalized cusp in AdS4 × CP³ and more oneloop results from semiclassical strings
, 2014
"... We evaluate the exact oneloop partition function for fundamental strings whose worldsurface ends on a cusp at the boundary of AdS4 and has a “jump” in CP³. This allows us to extract the stringy prediction for the ABJM generalized cusp anomalous dimension ΓABJMcusp (φ, θ) up to NLO in sigmamodel p ..."
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We evaluate the exact oneloop partition function for fundamental strings whose worldsurface ends on a cusp at the boundary of AdS4 and has a “jump” in CP³. This allows us to extract the stringy prediction for the ABJM generalized cusp anomalous dimension ΓABJMcusp (φ, θ) up to NLO in sigmamodel perturbation theory. With a similar analysis, we present the exact partition functions for folded closed string solutions moving in the AdS3 parts of AdS4×CP³ and AdS3×S3×S3×S1 backgrounds. Results are obtained applying to the string solutions relevant for the AdS4/CFT3 and AdS3/CFT2 correspondence the tools previously developed for their AdS5 × S5 counterparts.
Preprint typeset in JHEP style PAPER VERSION Scattering of single spikes
, 710
"... Abstract: We apply the dressing method to a string solution given by a static string wrapped around the equator of a threesphere and find that the result is the single spike solution recently discussed in the literature. Further application of the method allows the construction of solutions with mu ..."
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Abstract: We apply the dressing method to a string solution given by a static string wrapped around the equator of a threesphere and find that the result is the single spike solution recently discussed in the literature. Further application of the method allows the construction of solutions with multiple spikes. In particular we construct the solution describing the scattering of two single spikes and compute the scattering phase shift. As a function of the dressing parameters, the result is exactly the same as the one for the giant magnon, up to nonlogarithmic terms. This suggests that the single spikes should be described by an integrable spin chain closely related to the one associated to the giant magnons. The field theory interpretation of such spin chain however is still unclear. Keywords: Classical string solutions, AdS/CFT, spin chains, integrable systems. Contents
The Subleading Term of the Strong Coupling Expansion of the HeavyQuark Potential in a N = 4 Super YangMills Vacuum
, 905
"... Abstract: Applying the AdS/CFT correspondence, the expansion of the heavyquark potential of the N = 4 supersymmetric YangMills theory at large Nc is carried out to the subleading term in the large ’t Hooft coupling at zero temperature. The strong coupling corresponds to the semiclassical expansio ..."
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Abstract: Applying the AdS/CFT correspondence, the expansion of the heavyquark potential of the N = 4 supersymmetric YangMills theory at large Nc is carried out to the subleading term in the large ’t Hooft coupling at zero temperature. The strong coupling corresponds to the semiclassical expansion of the stringsigma model, the gravity dual of the Wilson loop operator, with the subleading term expressed in terms of functional determinants of fluctuations. The singularities of these determinants are examined and their contributions are evaluated numerically.
Dressed Wilson Loops on S2
"... We present a new, twoparameter family of string solutions corresponding to the holographic duals of specific 1/8BPS Wilson loops on S2 in N = 4 supersymmetric YangMills theory. The solutions are obtained using the dressing method on the known longitude solution in the context of the auxiliary σ ..."
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We present a new, twoparameter family of string solutions corresponding to the holographic duals of specific 1/8BPS Wilson loops on S2 in N = 4 supersymmetric YangMills theory. The solutions are obtained using the dressing method on the known longitude solution in the context of the auxiliary σmodel on S3 put forth in arXiv:0905.0665[hepth]. We verify that the regularized area of the worldsheets are consistent with expectations. ar X iv