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Spheres, charges, instantons, and bootstrap: a five-dimensional odyssey. (English) Zbl 1388.81740

Summary: 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.

MSC:

81T50 Anomalies in quantum field theory
83E30 String and superstring theories in gravitational theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
35Q51 Soliton equations
81T60 Supersymmetric field theories in quantum mechanics

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References:

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