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\( \mathcal{N} = 2 \) superconformal blocks and instanton partition functions

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Abstract

We consider the problem of computing (irregular) conformal blocks in 2d CFTs whose chiral symmetry algebra is the \( \mathcal{N} = 2 \) superconformal algebra.

Our construction uses two ingredients: (i) the relation between the representation the-ories of the \( \mathcal{N} = 2 \) superconformal algebra and the affine \( \widehat{\text{sl}} \)(2) algebra, extended to the level of the conformal blocks, and (ii) the relation between \( \widehat{\text{sl}} \)(2) conformal blocks and instanton partition functions in the 4d \( \mathcal{N} = 2 \) SU(2) gauge theory with a surface defect. By combining these two facts we derive combinatorial expressions for the \( \mathcal{N} = 2 \) superconformal blocks in the Gaiotto limit.

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  1. Theoretical Department, Lebedev Physical Institute, RAS, Moscow, Russia

    V. Belavin & Niclas Wyllard

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  2. Niclas Wyllard
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Correspondence to V. Belavin.

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ArXiv ePrint: 1205.3091

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Belavin, V., Wyllard, N. \( \mathcal{N} = 2 \) superconformal blocks and instanton partition functions. J. High Energ. Phys. 2012, 173 (2012). https://doi.org/10.1007/JHEP06(2012)173

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