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

TL;DR

This paper combines supersymmetric localization and conformal bootstrap to analyze five-dimensional superconformal field theories, revealing new anomalies, relations, and bounds that deepen understanding of their structure and spectra.

Contribution

It introduces a new superconformal anomaly, a triple factorization formula for the five-sphere partition function, and provides numerical evidence for bootstrap bounds in 5D SCFTs.

Findings

Discovery of a new superconformal anomaly in five dimensions

Derivation of a relation between partition function and central charges

Numerical evidence for bootstrap bounds saturation in specific theories

Abstract

We combine supersymmetric localization and the conformal bootstrap to study five-dimensional superconformal field theories. To begin, we classify the admissible counter-terms 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.