Abstract
The Schur limit of the superconformal index of four-dimensional \( \mathcal{N} \) = 2 superconformal field theories has been shown to equal the supercharacter of the vacuum module of their associated chiral algebra. Applying localization techniques to the theory suitably put on S3 × S1, we obtain a direct derivation of this fact. We also show that the localization computation can be extended to calculate correlation functions of a subset of local operators, namely of the so-called Schur operators. Such correlators correspond to insertions of chiral algebra fields in the trace-formula computing the supercharacter. As a by-product of our analysis, we show that the standard lore in the localization literature stating that only off-shell supersymmetrically closed observables are amenable to localization, is incomplete, and we demonstrate how insertions of fermionic operators can be incorporated in the computation.
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Pan, Y., Peelaers, W. Schur correlation functions on S3 × S1. J. High Energ. Phys. 2019, 13 (2019). https://doi.org/10.1007/JHEP07(2019)013
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DOI: https://doi.org/10.1007/JHEP07(2019)013