Speaker
Satoshi Yamaguchi
(Osaka U.)
Description
Lattice field theory provides one of the most reliable nonperturbative regularizations of quantum field theory. Meanwhile, the eta invariant of the Dirac operator, defined as a regularized sum of the signs of its eigenvalues, plays an important role in symmetry-protected topological phases and in anomalies in quantum field theories. In this talk, we investigate how the eta invariant can be formulated within lattice field theory. In particular, we construct a lattice formulation of the Arf–Brown–Kervaire (ABK) invariant in two dimensions. Domain walls, or interfaces, are useful tools for studying the ABK invariant on surfaces with boundaries.