Abstract
This is the first in a series of papers on the search for the 2D CFT description of a large class of 4D \( \mathcal{N}=1 \) gauge theories. Here, we identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks of the Virasoro/W-algebra, that underlie the 2D theory and reproduce the Seiberg-Witten curves of the \( \mathcal{N}=1 \) gauge theories. We find that the blocks corresponding to the SU(N) \( {\mathcal{S}}_k \) gauge theories involve fields in certain non-unitary representations of the W kN algebra. These conformal blocks give a prediction for the instanton partition functions of the 4D \( \mathcal{N}=1 \) SCFTs of class \( {\mathcal{S}}_k \).
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Mitev, V., Pomoni, E. 2D CFT blocks for the 4D class \( {\mathcal{S}}_k \) theories. J. High Energ. Phys. 2017, 9 (2017). https://doi.org/10.1007/JHEP08(2017)009
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DOI: https://doi.org/10.1007/JHEP08(2017)009