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

Abstract

Abstract We consider $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 2 vector multiplet, it has been shown that the 2-point functions in the sector of chiral primaries (Trφ 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 $$ \mathcal{N} $$ 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 $$ \mathcal{O} $$ O (λ10) 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 (Trφ 2) n Trφ 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 $$ \mathcal{O} $$ O (λ 7) and generic N. Large N factorization is also illustrated as a check of the computation.