2024/03/06 by Philip Boyle Smith, Smith, Philip Boyle, Yunqin Zheng +1 · 2 citations
Physics and Astronomy · Social Sciences · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #International Science and Diplomacy #Quantum Chromodynamics and Particle Interactions #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2403.03953
openalex publication_date 2024/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a fermionic quantum field theory in d=1+1 dimensions, there is a subtle difference between summing over spin structures and gauging (-1)F. If the gravitational anomaly vanishes mod 16, then both operations are equivalent and yield a bosonic theory. But if the gravitational anomaly only vanishes mod 8, then only gauging (-1)F is allowed, and the result is a fermionic theory. Our goal is to understand in detail how this happens, despite the fact (-1)F is defined in terms of shifting the spin structure, which would naïvely suggest that both operations are equivalent. We do this from three perspectives: an abstract view in terms of anomalies, explicit CFT calculations, and a Symmetry TFT perspective. To conclude, we illustrate our results using the heterotic string and the famous self-triality of 8 Majorana-Weyl fermions.