Abstract
We present a new non-perturbative ’t Hooft anomaly afflicting a quantum field theory with symmetry group G = U(1) × ℤ2 in four dimensions. We use the Adams spectral sequence to compute that the bordism group \({\Omega }_{5}^{{\text{Spin}}}\)(BG), which classifies anomalies that remain when perturbative anomalies cancel, is ℤ4. By constructing a mapping torus and evaluating the Atiyah-Patodi-Singer η-invariant, we show that the mod 4 anomaly is generated by a pair of Weyl fermions that are vector-like under U(1), but with only one component charged under ℤ2. We construct a simple microscopic field theory that realises the anomaly, before investigating its impact in the hydrodynamic limit. We find that the anomaly dictates transport phenomena in the U(1) current and energy-momentum tensor akin to the chiral vortical and magnetic effects (even though the perturbative anomalies here vanish), but with the conductivities being fractionally quantised in units of a quarter, reflecting the mod 4 nature of the bordism group. Along the way, we compute the (relevant) bordism groups \({\Omega }_{d}^{{\text{Spin}}}\)(Bℤ2 × BU(1)) and \({\Omega }_{d}^{{{\text{Pin}}}^{-}}\) (BU(1)) in all degrees d = 0 through 5.
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Acknowledgments
We would like to thank Iñaki García-Etxebarria, Nabil Iqbal, Akash Jain, Tin Sulejmanpasic and David Tong for various discussions on this topic, as well as Karl Landsteiner and David Tong for their comments on our manuscript. NL is supported by the STFC consolidated grant in Particles, Strings and Cosmology number ST/T000708/1 and the Royal Society of London. The work of NP is supported by the grant for development of new faculty (Ratchadapiseksomphot fund) and Sci-Super IX 66 004 from Chulalongkorn University and is grateful to the hospitality of Durham University and NORDITA during the course of this work. NL and NP also wish to thank the “Paths to Quantum Field Theory 2023” workshop for hospitality during part of this project.
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Davighi, J., Lohitsiri, N. & Poovuttikul, N. A non-perturbative mixed anomaly and fractional hydrodynamic transport. J. High Energ. Phys. 2024, 119 (2024). https://doi.org/10.1007/JHEP03(2024)119
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DOI: https://doi.org/10.1007/JHEP03(2024)119