Bordism computation for K(Z,3) identifies a new mixed perturbative anomaly in 5D and a new Z2 discrete anomaly in 7D for U(1) 1-form symmetries.
Eta-Invariants and Determinant Lines
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study eta-invariants on odd dimensional manifolds with boundary. The dependence on boundary conditions is best summarized by viewing the (exponentiated) eta-invariant as an element of the (inverse) determinant line of the boundary. We prove a gluing law and a variation formula for this invariant. This yields a new, simpler proof of the holonomy formula for the determinant line bundle of a family of Dirac operators, also known as the ``global anomaly'' formula. This paper is written using AMSTeX 2.1, which can be obtained via ftp from the American Mathematical Society (instructions included). A postscript file with figures was submitted separately in uuencoded tar-compressed format.
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On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies
Bordism computation for K(Z,3) identifies a new mixed perturbative anomaly in 5D and a new Z2 discrete anomaly in 7D for U(1) 1-form symmetries.
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Anomaly-Free Spectra, Unimodular Lattices and 6D R-Symmetry Gauged Supergravity
Eleven new anomaly-free 6D (1,0) supergravities with G_non-Abelian × U(1)_R are found that satisfy Green-Schwarz factorization and global consistency conditions, together with proofs of n_V ≡ 8 mod 12 necessity for rank-two unimodular embeddability (absent SU(2), SU(3), G2).
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Symmetry TFTs from String Theory
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What makes spacetime spin in string theory?
GSO projection consistency in Type II string theory requires the target space X to admit a spin structure (or G-equivariant spin structure for orbifolds), identified by computing the mixed bordism group Ω₃^spin(Bℤ₂ × X) and classifying corresponding theta angles.
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WIMP Dark Matter from a Natural Discrete Gauge Symmetry in the Standard Model
A Z4 × Z3 discrete gauge symmetry in the SM requires three new Majorana fermions whose lightest member is stable DM with mass from a singlet scalar VEV near the electroweak scale, enabling WIMP freeze-out via scalar-mediated annihilation.
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Anomalies in family unification models from bordism classification
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