de Mello Koch Robert, Rabambi Phumudzo, Rabe Randle, Ramgoolam Sanjaye
School of Physics and Mandelstam Institute for Theoretical Physics, University of Witwatersrand, Wits, 2050, South Africa.
Centre for Research in String Theory and School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS United Kingdom.
Phys Rev Lett. 2017 Oct 20;119(16):161602. doi: 10.1103/PhysRevLett.119.161602. Epub 2017 Oct 16.
We develop general counting formulas 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 multivariable 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 orbifolds. We construct the unique 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.
我们推导了自由四维（4D）标量共形场论（CFT）中基本场的一般计数公式。通过标量场论中的基本算符与受微分约束的多变量多项式函数之间的对偶映射，我们确定了一类全纯基本场的扇区，其对应于一类置换orbifold上的多项式函数。这些orbifold具有回文希尔伯特级数，这表明它们是卡拉比 - 丘orbifold。我们构造了卡拉比 - 丘性质所预期的唯一最高维全纯形式。这个扇区包含并扩展了先前对无限基本场族的构造。我们概述了将这些结果推广到自由4D矢量和矩阵CFT的情况。
