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

  • Matteo BeccariaEmail author
Open Access
Regular Article - Theoretical Physics
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Abstract

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 (Trφ2)n admit a finite limit when gYM → 0 with large R-charge growing like ∼ 1/g YM 2 . The correction with respect to \( \mathcal{N} \) = 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 \( \mathcal{O} \)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 (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 \( \mathcal{O} \)(λ7) and generic N. Large N factorization is also illustrated as a check of the computation.

Keywords

Extended Supersymmetry Matrix Models 

Notes

Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento & INFNLecceItaly

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