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

A bstract We consider N N = 2 SU( N ) SQCD in four dimensions and a weak-coupling regime with large R-charge recently discussed in arXiv:1803.00580 . If φ denotes the adjoint scalar in the N N = 2 vector multiplet, it has been shown that the 2-point functions in the sector of chiral primaries (Tr φ 2 ) n admit a finite limit when g YM → 0 with large R-charge growing like ∼ 1/g YM 2 . The correction with respect to N N = 4 correlators is a non-trivial function F ( λ ; N ) of the fixed coupling λ = n g YM 2 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 (λ; N ) at order O O (λ 10 ) for generic N , greatly extending previous results and placing on a firmer 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 φ 2 ) n Tr φ 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 O ( λ 7 ) and generic N . Large N factorization is also illustrated as a check of the computation.