A bordism computation for K(Z,3) produces two new anomaly classes for U(1) 1-form symmetries: a mixed H₃∧p₁ anomaly in 5d and a Z₂-valued uSq²u anomaly in 7d.
Anomaly Inflow and the η-Invariant
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Derives a residue formula for elliptic genera in 2d (0,1) gauge theories that recovers the Jeffrey-Kirwan prescription for (0,2) theories and applies it to the Gukov-Pei-Putrov model to study its phase structure.
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.
Proposes a bosonized lattice construction of anomaly-free 2D non-Abelian chiral gauge theories in which left and right bulk contributions cancel at finite spacing when quadratic indices match.
Family unification models from E7 cosets have no global sigma model anomalies because the torsion parts of their bordism groups vanish, as computed via the Atiyah-Hirzebruch spectral sequence, including when isotropy subgroups are gauged.
Superconductors are bosonic at low energy yet carry a gravito-magnetic anomaly from fermion parity gauging that forbids trivial massive phases in 3D and 4D.
The authors establish the descendant structure of the holographic SO(2,d) anomaly and construct the associated characteristic class, bulk Chern-Simons-like action, boundary effective action, and anomalous conservation laws in covariant and consistent forms.
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
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On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies
A bordism computation for K(Z,3) produces two new anomaly classes for U(1) 1-form symmetries: a mixed H₃∧p₁ anomaly in 5d and a Z₂-valued uSq²u anomaly in 7d.
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Elliptic Genera of 2d $\mathcal{N}=(0,1)$ Gauge Theories
Derives a residue formula for elliptic genera in 2d (0,1) gauge theories that recovers the Jeffrey-Kirwan prescription for (0,2) theories and applies it to the Gukov-Pei-Putrov model to study its phase structure.
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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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Lattice chiral non-Abelian gauge symmetry via bosonization
Proposes a bosonized lattice construction of anomaly-free 2D non-Abelian chiral gauge theories in which left and right bulk contributions cancel at finite spacing when quadratic indices match.
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Anomalies in family unification models from bordism classification
Family unification models from E7 cosets have no global sigma model anomalies because the torsion parts of their bordism groups vanish, as computed via the Atiyah-Hirzebruch spectral sequence, including when isotropy subgroups are gauged.
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Gauging in superconductors and other electronic systems
Superconductors are bosonic at low energy yet carry a gravito-magnetic anomaly from fermion parity gauging that forbids trivial massive phases in 3D and 4D.
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Holographic $SO(2,d)$ anomaly
The authors establish the descendant structure of the holographic SO(2,d) anomaly and construct the associated characteristic class, bulk Chern-Simons-like action, boundary effective action, and anomalous conservation laws in covariant and consistent forms.
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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.