Bootstrapping ABJM theory

TL;DR

This paper develops a bootstrap framework to systematically compute instanton corrections in ABJM theory, providing analytic derivations of relations for free energy and Wilson loops, and revealing new structural features of nonperturbative effects.

Contribution

It introduces a novel bootstrap approach for calculating instanton corrections in ABJM theory, extending previous conjectures with analytic derivations and structural insights.

Findings

Derived relations for free energy previously known only conjecturally

Determined nonperturbative corrections to BPS Wilson loops

Uncovered new structural features of instanton effects in ABJM

Abstract

Supersymmetric localization reduces the computation of protected observables in ABJM theory to finite-dimensional matrix integrals. Building on the techniques introduced in arXiv:2512.02119, we develop a bootstrap framework for the systematic calculation of instanton corrections to the free energy and to supersymmetric Wilson loops. Exploiting exact functional relations and consistency conditions satisfied by grand-canonical observables, in the Fermi-gas formulation of the ABJM matrix model, we provide analytic derivations of several relations for the free energy that were previously known only conjecturally, either from refined topological string theory or from high-precision numerical studies. We apply the same framework to determine the nonperturbative corrections to $1/2$ and $1/6$ BPS Wilson loops, elucidating their qualitative differences and uncovering novel structural features of the instanton effects. These results further highlight the intricate nonperturbative structure and network of dualities underlying ABJM theory.