A formula for the block expansion in free CFTs and applications to \cal N=4 SYM at strong coupling

2025/02/19 by Aprile, F., Drummond, J. M., Heslop, P. J. +1 · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2502.14077

Abstract

An explicit analytic formula is presented that computes the conformal (super-)block decomposition of any free scalar or half-BPS diagram in 1d, 2d or 4d CFTs, with various supersymmetries, including none. We prove our formula by exploiting a connection between conformal blocks and symmetric polynomials. Then we give a direct application of our result to the study of four-point correlators in \cal N=4 SYM at strong coupling. In particular, we give a CFT proof of the tree-level Witten diagram representation of ⟨ \cal O₂²\cal O₂² \cal O_q\cal O_q⟩ on AdS₅×S⁵, providing new and highly non-trivial checks of the AdS/CFT correspondence. Our method works for a more general class of multi-particle correlators and can be used to bootstrap new results at strong coupling.

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