Bootstrapping ABJM theory

TL;DR

The paper develops a bootstrap framework within the ABJM matrix model, recasting observables via a Fermi-gas formalism to enable analytic control over nonperturbative instanton corrections. Central to the approach are exact relations, quantization conditions, and an effective chemical potential $\mu_{\mathrm{eff}}$, which organize world-sheet and membrane instanton contributions into a structured expansion in $Q_{\mathrm w}$ and $Q_{\mathrm m}$. The authors derive first-principle analytic expressions for the grand potential and for $1/2$ and $1/6$ BPS Wilson loops, clarifying how membrane effects enter and how pole cancellation constrains the nonperturbative data, thereby validating and extending previous conjectures from refined topological string theory and numerical studies. The results reveal a rich nonperturbative structure and duality network in ABJM theory, with implications for connections to NS/topological-string periods and potential generalizations to other observables and deformations.

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.