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Differential equations for Wilson loops in ABJM theory

Takao Suyama*

  • *Contact author: suyama.takao@nihon-u.ac.jp
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Phys. Rev. D 113, 026019 – Published 23 January, 2026

DOI: https://doi.org/10.1103/f8t8-v2rp

Abstract

We derive a system of differential equations which are satisfied by the vacuum expectation values (vevs) of BPS Wilson loops and ’t Hooft coupling of ABJM theory. They are Picard-Fuchs equations of an algebraic curve defined by the derivative of the planar resolvent of the corresponding matrix model. The weak and strong coupling behaviors can be reproduced by their local solutions around regular singularities. We also obtain a recursion relation which can be used to determine the planar vevs of BPS Wilson loops in arbitrary representations.

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Phys. Rev. D 113, 026019– Published 23 January, 2026
  • Received 2 December 2025
  • Accepted 2 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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