On the large R-charge $\mathcal N=2$ chiral correlators and the Toda equation

Understand

We consider $\mathcal N=2$ $SU(N)$ SQCD in four dimensions and a weak-coupling regime with large R-charge recently discussed in arXiv:1803.00580.

• If $\varphi$ denotes the adjoint scalar in the $\mathcal N=2$ vector multiplet, it has been shown that the 2-point functions in the sector of chiral primaries $(\text{Tr} \varphi^2)^n$ admit a finite limit when $g_\text{YM}\to 0$ with large R-charge growing like $\sim 1/g^2_\text{YM}$.
• The correction with respect to $\mathcal N=4$ correlators is a non-trivial function $F(\lambda; N)$ of the fixed coupling $\lambda=n\,g^2_\text{YM}$ and the gauge algebra rank $N$.
• We show how to exploit the Toda equation following from the $tt^*$ equations in order to control the R-charge dependence.