Abstract
We consider an analogue of Witten’s SL(2, ℤ) action on three-dimensional QFTs with U(1) symmetry for 2k-dimensional QFTs with ℤ2 (k − 1)-form symmetry. We show that the SL(2, ℤ) action only closes up to a multiplication by an invertible topological phase whose partition function is the Brown-Kervaire invariant of the spacetime manifold. We interpret it as part of the SL(2, ℤ) anomaly of the bulk (2k + 1)-dimensional ℤ2 gauge theory.
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Bhardwaj, L., Lee, Y. & Tachikawa, Y. SL(2, ℤ) action on QFTs with ℤ2 symmetry and the Brown-Kervaire invariants. J. High Energ. Phys. 2020, 141 (2020). https://doi.org/10.1007/JHEP11(2020)141
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DOI: https://doi.org/10.1007/JHEP11(2020)141