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"... We study the supersymmetric circular Wilson loops of N = 4 super Yang-Mills in large representations of the gauge group. In particular, we obtain the spectral curves of the matrix model which captures the expectation value of the loops. These spectral curves are then proven to be precisely the hyper ..."

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We study the supersymmetric circular Wilson loops of N = 4 super Yang-Mills in large representations of the gauge group. In particular, we obtain the spectral curves of the matrix model which captures the expectation value of the loops. These spectral curves are then proven to be precisely the hyperelliptic surfaces that characterize the bubbling solutions dual to the Wilson loops, thus yielding an example of a geometry emerging from an eigenvalue distribution. We finally discuss the Wilson loop expectation value from the matrix model and from supergravity. Contents

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"... We study the supersymmetric circular Wilson loops of N = 4 super Yang-Mills in large representations of the gauge group. In particular, we obtain the spectral curves of the matrix model which captures the expectation value of the loops. These spectral curves are then proven to be precisely the hyper ..."

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We study the supersymmetric circular Wilson loops of N = 4 super Yang-Mills in large representations of the gauge group. In particular, we obtain the spectral curves of the matrix model which captures the expectation value of the loops. These spectral curves are then proven to be precisely the hyperelliptic surfaces that characterize the bubbling solutions dual to the Wilson loops, thus yielding an example of a geometry emerging from an eigenvalue distribution. We finally discuss the Wilson loop expectation value from the matrix model and from supergravity. Contents

### Supersymmetric Wilson Loops in Diverse Dimensions

, 904

"... We consider supersymmetric Wilson loops à la Zarembo in planar supersymmetric Yang-Mills theories in diverse dimensions. Using perturbation theory we show that these loops have trivial vacuum expectation values to second order in the ’t Hooft coupling. We review the known superspace results which, f ..."

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We consider supersymmetric Wilson loops à la Zarembo in planar supersymmetric Yang-Mills theories in diverse dimensions. Using perturbation theory we show that these loops have trivial vacuum expectation values to second order in the ’t Hooft coupling. We review the known superspace results which, for specific dimensions, extend this triviality to all orders in the ’t Hooft coupling. Using the gauge/gravity correspondence, we construct the explicit dual fundamental string solutions corresponding to these Wilson loops for the case of circular geometry. We find that the regularized action of these string solutions vanishes. We also generalize the framework of calibrated surfaces to prove the vanishing of the regularized action for loops of general geometry. We propose a possible string-side manifestation of the gauge theory generalized Konishi By now there is mounting evidence in favor of both the usefulness as well as the validity of the gauge/gravity duality between N = 4 SYM in four dimensions and string

### NSF-KITP-08-96

, 807

"... Wilson loop correlators at strong coupling: from matrices to bubbling geometries ..."

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Wilson loop correlators at strong coupling: from matrices to bubbling geometries

### Dressed Wilson Loops on S2

"... We present a new, two-parameter family of string solutions corresponding to the holographic duals of specific 1/8-BPS Wilson loops on S2 in N = 4 su-persymmetric Yang-Mills 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, two-parameter family of string solutions corresponding to the holographic duals of specific 1/8-BPS Wilson loops on S2 in N = 4 su-persymmetric Yang-Mills theory. The solutions are obtained using the dressing method on the known longitude solution in the context of the auxiliary σ-model on S3 put forth in arXiv:0905.0665[hep-th]. We verify that the regularized area of the world-sheets are consistent with expectations. ar X iv