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arXiv · 2003.13343

Superconformal Block from Holographic Geometry

Heng-Yu Chen·Jun-ichi Sakamoto
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Abstract

We explicitly construct the holographic dual configuration for the four dimensional $\mathcal{N}=4$ superconformal block containing half-BPS scalar primary operators by considering its full $AdS_5 \times S^5$ dual geometry. We extend the embedding space formalism and the related Harmonic analysis to general $d$-dimensional sphere $S^d$, and obtain precisely the $R$-symmetry contribution to the half-BPS scalar superconformal blocks, which we refer as "$R$-symmetry block". We also observe that the $R$-symmetry quadratic Casimir operator can be mapped to BC$_{2}$ Calogero-Sutherland system Hamiltonian, such that $R$-symmetry block is in terms identified as its bound state wave function.

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Heng-Yu Chen, Jun-ichi Sakamoto. 2020-03-30. Superconformal Block from Holographic Geometry. https://doi.org/10.1007/jhep07(2020)028

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