On the large R-charge=2 chiral correlators and the Toda equation

We consider N = 2 SU(N) SQCD in four dimensions and a weak-coupling regime with large R-charge recently discussed in arXiv:1803.00580. If ' denotes the adjoint scalar in the N = 2 vector multiplet, it has been shown that the 2-point functions in the sector of chiral primaries (Tr '2) n admit a fi nite limit when gYM ! 0 with large R-charge growing like 1 =g2 YM. The correction with respect to N = 4 correlators is a non-trivial function F (; N) of the fi xed coupling = n g2 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. This allows to determine F (; N) at order O (10) for generic N, greatly extending previous results and placing on a fi rmer ground a conjecture proposed for the SU(2) case. We show that a similar Toda equation, discussed in the past, may indeed be used for the additional sector (Tr '2) n Tr '3 due to the special mixing properties of these composite operators on the 4-sphere. We discuss the large R-limit in this second case and compute the associated scaling function F at order O (7) and generic N. Large N factorization is also illustrated as a check of the computation.