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arXiv · 1705.04039

Free quantum fields in 4D and Calabi-Yau spaces

Robert de Mello Koch·Phumudzo Rabambi·Randle Rabe·Sanjaye Ramgoolam
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Abstract

We develop general counting formulae for primary fields in free four dimensional (4D) scalar conformal field theory (CFT). Using a duality map between primary operators in scalar field theory and multi-variable polynomial functions subject to differential constraints, we identify a sector of holomorphic primary fields corresponding to polynomial functions on a class of permutation orbifolds. These orbifolds have palindromic Hilbert series, which indicates they are Calabi-Yau. We construct the top-dimensional holomorphic form expected from the Calabi-Yau property. This sector includes and extends previous constructions of infinite families of primary fields. We sketch the generalization of these results to free 4D vector and matrix CFTs.

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Robert de Mello Koch, Phumudzo Rabambi, Randle Rabe, Sanjaye Ramgoolam. 2017-05-11. Free quantum fields in 4D and Calabi-Yau spaces. https://doi.org/10.1103/physrevlett.119.161602

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