Abstract
We consider \( \mathcal{N} \) = 2 conformal QCD in four dimensions and the one-point correlator of a class of chiral primaries with the circular \( \frac{1}{2} \)-BPS Maldacena-Wilson loop. We analyze a recently introduced double scaling limit where the gauge coupling is weak while the R-charge of the chiral primary Φ is large. In particular, we consider the case Φ = (Trφ2)n, where φ is the complex scalar in the vector multiplet. The correlator defines a non-trivial scaling function at fixed κ = ng 2YM and large n that may be studied by localization. For any gauge group SU(N) we provide the analytic expression of the first correction ~ ζ(3)κ2 and prove its universality. In the SU(2) and SU(3) theories we compute the scaling functions at order \( \mathcal{O} \)(κ6). Remarkably, in the SU(2) case the scaling – function is equal to an analogous quantity describing the chiral 2-point functions \( \left\langle \Phi \overline{\Phi}\right\rangle \) in the same large R-charge limit. We conjecture that this SU(2) scaling function is computed at all-orders by a \( \mathcal{N} \) = 4 SYM expectation value of a matrix model object characterizing the one-loop contribution to the 4-sphere partition function. The conjecture provides an explicit series expansion for the scaling function and is checked at order \( \mathcal{O} \)(κ10) by showing agreement with the available data in the sector of chiral 2-point functions.
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Beccaria, M. Double scaling limit of \( \mathcal{N} \)= 2 chiral correlators with Maldacena-Wilson loop. J. High Energ. Phys. 2019, 95 (2019). https://doi.org/10.1007/JHEP02(2019)095
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DOI: https://doi.org/10.1007/JHEP02(2019)095