Subleading Corrections in N=3 Gaiotto-Tomasiello Theory

TL;DR

This paper analyzes subleading corrections to the free energy of the $ =3$ Gaiotto-Tomasiello theory, providing explicit expansions and numerical verification for specific cases of equal rank and levels.

Contribution

It derives parametric equations for the free energy and endpoints, and presents explicit perturbative and full expressions for special cases, advancing understanding of subleading effects in this theory.

Findings

Explicit parametric equations for free energy and endpoints.

Perturbative expansion for equal rank gauge groups.

Full expression for free energy when both groups have equal levels.

Abstract

We study subleading corrections to the genus-zero free energy of the $\mathcal{N}=3$ Gaiotto-Tomasiello theory. In general, we obtain the endpoints and free energy as a set of parametric equations via contour integrals of the planar resolvent, up to exponentially suppressed corrections. In the particular case that the two gauge groups in the quiver are of equal rank, we find an explicit (perturbative) expansion for the free energy. If, additionally, both groups have equal levels, then we find the full expression for the genus-zero free energy, modulo exponentially suppressed corrections. We also verify our results numerically.