Gravity duals of half-BPS Wilson loops

By E. D’Hoker, John W. Estes, M. Gutperle. 2007

187 citations recorded by the source corpus.

We explicitly construct the fully back-reacted half-BPS solutions in Type IIB supergravity which are dual to Wilson loops with 16 supersymmetries in = 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 AdS2 × S2 × S4 × Σ, with isometry group SO(2, 1) × SO(3) × SO(5) in terms of two locally harmonic functions on a Riemann surface Σ 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 ≥ 0 hyperelliptic surface Σ, all of whose branch points lie on the real line. Each genus g solution has only a single asymptotic AdS5 × S5 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 AdS5 × S5 with 3 free parameters, while for genus g ≥ 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 Σ 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.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/13c334b8b3502e20c959995f3024372b96799039

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In Applied Mathematics

1. M. Gutperle
2. E. D’Hoker
3. John W. Estes
4. C. Uhlemann

In Geometry and Topology

1. M. Gutperle
2. E. D’Hoker
3. John W. Estes
4. C. Uhlemann

In Nuclear and High Energy Physics

1. E. D’Hoker
2. M. Gutperle
3. John W. Estes
4. C. Uhlemann
5. Eric Perlmutter
6. Per Kraus
7. D. Gaiotto
8. E. Witten

Citations in the corpus

• Exact half-BPS type IIB interface solutions II: flux solutions and multi-Janus (2007, methodology): “terpreted as the fully back reacted geometry dual to half-BPS Wilson loops [6, 7, 8]. A detailed analysis of this solution applying the methods of this paper can be found in a further companion paper [9]. Acknowledgements We are happy to acknowledge a useful conversation with George Morales on plana”
• Warped AdS6 × S2 in Type IIB supergravity II: global solutions and five-brane webs (2017, methodology): “e by the choice of two locally holomorphic functions A on a two-dimensional Riemann surface whose global structure is as yet undetermined.1 In [1], we followed the strategy developed some time ago in [16,17,18], and utilized the integrable structure of the reduced BPS equations [19] along with the h”
• Exact half-BPS Type IIB interface solutions. I. Local solution and supersymmetric Janus (2007, methodology): “A detailed analysis of this solution applying the methods of this paper can be found in a further companion paper [37].”