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SUMMARY:Seminar\, Sho Araki (荒木 匠\, Osaka U.)
DTSTART;VALUE=DATE-TIME:20260521T043000Z
DTEND;VALUE=DATE-TIME:20260521T053000Z
UID:205440172619
DESCRIPTION:Title: The Arf–Brown–Kervaire (ABK) Invariant in Lattice F
 ermion Systems\n\nAbstract: Topological invariants in fermionic systems pr
 ovide sharp probes of symmetry and anomaly. In this talk\, we study how to
  formulate such a topological invariant that is valued in Z_8\, known as t
 he Arf-Brown-Kervaire (ABK) invariant\, for the lattice fermion systems. T
 he ABK invariant is a two-dimensional invariant that is encoded in the com
 plex phase of the Majorana fermion partition function\, and it plays a rol
 e analogous to topological terms such as the instanton number in 4D Dirac 
 fermion settings. We employ massive Wilson Dirac operators and numerically
  demonstrate that the ABK invariant emarges on the partition function. To 
 capture the ABK invariant fully\, it is essential to consider various type
 s of manifold including non-orientable ones such as the real projective pl
 ane and the Klein bottle. In addition\, manifolds with boundaries are also
  important for understanding anomaly and anomaly inflow. We discuss how to
  realize the geometries of these manifolds on the lattice and verify numer
 ically (and partly analytically) that our formulation reproduces the known
  values in continuum theory.
LOCATION:721
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