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Title:
Quantum Reflections in 3D QFTs and their Local Spin(7) Counterparts
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Abstract:
Compactifications of M-theory on local Spin(7) spaces with singularities provide a flexible framework for realizing 3D quantum field theories (QFTs). We explain how physical anomalies associated with reflections translate in the local Spin(7) geometry to certain index-theoretic structures which take values mod 16 rather than over the integers. This is in contrast with the case of M-theory on a local G2 space and F-theory on an elliptically fibered Calabi-Yau fourfold, where the analogous indices for 4D quantum field theories take values over the integers. Our primary tool used to establish this correspondence involves Higgs bundles on four-manifolds and three-manifolds. Based on joint work with M. Cvetic, E. Torres and G. Zoccarato.
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