Gravity duals of half-BPS Wilson loops

Abstract

We explicitly construct the fully back-reacted half-BPS solutions in Type IIB supergravity which are dual to Wilson loops with 16 supersymmetries in $\mathcal{N}=4$ super Yang-Mills. In a first part, we use the methods of a companion paper to derive the exact general solution of the half-BPS equations on the space $Ad{S}_2\times S^2\times S^4\times \Sigma$, with isometry group $SO(2,1)\times SO(3)\times SO(5)$ in terms of two locally harmonic functions on a Riemann surface $\Sigma$ with boundary. These solutions, generally, have varying dilaton and axion, and non-vanishing 3-form fluxes. In a second part, we impose regularity and topology conditions. These non-singular solutions may be parametrized by a genus $g\ge 0$ hyperelliptic surface $\Sigma$, all of whose branch points lie on the real line. Each genus $g$ solution has only a single asymptotic $Ad{S}_5\times S^5$ region, but exhibits $g$ homology 3-spheres, and an extra $g$ homology 5-spheres, carrying respectively RR 3-form and RR 5-form charges. For genus 0, we recover $Ad{S}_5\times S^5$ with 3 free parameters, while for genus $g\ge 1$, the solution has $2g+5$ free parameters. The genus 1 case is studied in detail. Numerical analysis is used to show that the solutions are regular throughout the $g=1$ parameter space. Collapse of a branch cut on $\Sigma$ subtending either a homology 3-sphere or a homology 5-sphere is non-singular and yields the genus $g-1$ solution. This behavior is precisely expected of a proper dual to a Wilson loop in gauge theory.

62 pages, LaTeX, 6 figures, v2: minor changes

References in corpus (6)

• Holographic Wilson Loops
• On gravitational description of Wilson lines
• Wilson Loops as D3-Branes
• Ten-dimensional supersymmetric Janus solutions
• Multiply wound Polyakov loops at strong coupling
• Bubbling Defect CFT's

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