Entropic F function of three-dimensional Ising conformal field theory via fuzzy sphere regularization

The F function, the three-dimensional counterpart of the central charge in the two-dimensional (2D) conformal field theory, measures the effective number of degrees of freedom in three-dimensional (3D) quantum field theory, and it is monotonically decreasing under the renormalization group flow. However, unlike the 2D central charge, the F function is a nonlocal quantity and cannot be computed using correlators of local operators. Utilizing the recently proposed fuzzy sphere regularization, we have performed the first nonperturbative computation of the F function for the paradigmatic 3D Ising conformal field theory through entanglement entropy. Our computation yields FIsing=0.0612(5), slightly smaller than the F function of a real free scalar, Ffree=log28-3ζ(3)16π2≈0.0638, consistent with the F theorem, and close to the 4-ϵ expansion estimates of FIsing≈0.061∼0.062.