Fredholm determinants and resurgence in supersymmetric theoriesTBA
by
In holographic dualities, non-perturbative contributions at large ’t Hooft coupling play an important role, as they encode different saddle point corrections for the string worldsheet. Recent work has established a systematic method for computing strong-coupling transseries to arbitrary order for a class of observables in four-dimensional planar N=2 and N=4 supersymmetric Yang–Mills theories. These observables can be expressed in terms of Fredholm determinants at arbitrary ’t Hooft coupling.
Building on these developments, I investigate the strong-coupling expansion of observables within this framework, including the octagon form factor and the cusp anomalous dimension. I present a universal structure governing their non-perturbative corrections, which enables the reconstruction of their full transseries from perturbative data alone. I also explore resurgence relations between non-perturbative sectors and show how the large-order behaviour of each sector encodes subleading exponential corrections.