Differential Equations for Wilson Loops in ABJM Theory

2025/09/20 by Takao Suyama, Suyama, Takao
Chemical Engineering · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum chaos and dynamical systems #Rheology and Fluid Dynamics Studies #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2509.16545

openalex publication_date 2025/09/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We derive a system of differential equations which are satisfied by the 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.

Citations

• Spectral Theory and Mirror Symmetry
• Topological Strings from Quantum Mechanics
• On the Gauge Theory/Geometry Correspondence
• The Large N Limit of Superconformal Field Theories and Supergravity

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