Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey

We combine supersymmetric localization and the conformal bootstrap to study fivedimensional superconformal field theories. To begin, we classify the admissible counterterms and derive a general relation between the five-sphere partition function and the conformal and flavor central charges. Along the way, we discover a new superconformal anomaly in five dimensions. We then propose a precise triple factorization formula for the five-sphere partition function, that incorporates instantons and is consistent with flavor symmetry enhancement. We numerically evaluate the central charges for the rank-one Seiberg and Morrison-Seiberg theories, and find strong evidence for their saturation of bootstrap bounds, thereby determining the spectra of long multiplets in these theories. Lastly, our results provide new evidence for the F -theorem and possibly a C-theorem in five-dimensional superconformal theories. ar X iv :1 71 0. 08 41 8v 1 [ he pth ] 2 3 O ct 2 01 7