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Notes on supersymmetric Wilson loops on a two-sphere

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Abstract

We study a recently discovered family of 1/8-BPS supersymmetric Wilson loops in \( \mathcal{N} = 4 \) super Yang-Mills theory and their string theory duals. The operators are defined for arbitrary contours on a two-sphere in space-time, and they were conjectured to be captured perturbatively by 2d bosonic Yang-Mills theory. In the AdS dual, they are described by pseudo-holomorphic string surfaces living on a certain submanifold of AdS 5 × S 5. We show that the regularized area of these string surfaces is invariant under area preserving diffeomorphisms of the boundary loop, in agreement with the conjecture. Further, we find a connection between the pseudo-holomorphicity equations and an auxiliary σ-model on S 3, which may help to construct new 1/8-BPS string solutions. We also show that the conjectured relation to 2d Yang-Mills implies that a connected correlator of two Wilson loops is computed by a Hermitian Gaussian two-matrix model. On the AdS dual side, we argue that the connected correlator is described by two disconnected disks interacting through the exchange of supergravity modes, and we show that this agrees with the strong coupling planar limit of the two-matrix model.

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Authors and Affiliations

  1. Center for the Fundamental Laws of Nature, Jefferson Physical Laboratory, Harvard University Physics Department, 17 Oxford Street, Cambridge, MA, 02138, U.S.A.

    Simone Giombi & Vasily Pestun

  2. Theoretical Physics Group, Blackett Laboratory, Imperial College, London, SW7 2AZ, U.K.

    Riccardo Ricci

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  1. Simone Giombi
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  2. Vasily Pestun
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Giombi, S., Pestun, V. & Ricci, R. Notes on supersymmetric Wilson loops on a two-sphere. J. High Energ. Phys. 2010, 88 (2010). https://doi.org/10.1007/JHEP07(2010)088

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