2018/09/30 by Matteo Beccaria
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep02(2019)009
27 pages. v2: minor clarifications added
arxiv created 2018/10/02 · arxiv updated 2019/02/20
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 φ 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 (Tr φ2)n admit a finite limit when gYM→ 0 with large R-charge growing like ∼ 1/g2YM. The correction with respect to \mathcal N=4 correlators is a non-trivial function F(λ; N) of the fixed coupling λ=n g2YM 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(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 (Trφ2)n Trφ3 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(λ7) and generic N. Large N factorization is also illustrated as a check of the computation.