Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.Comment: 8 pages, Proceedings of the 35th annual International Symposium on Lattice Field Theor

Atiyah-Patodi-Singer index on a lattice

We propose a non-perturbative formulation of the Atiyah-Patodi-Singer(APS) index in lattice gauge theory, in which the index is given by the $\eta$ invariant of the domain-wall Dirac operator. Our definition of the index is always an integer with a finite lattice spacing. To verify this proposal, using the eigenmode set of the free domain-wall fermion, we perturbatively show in the continuum limit that the curvature term in the APS theorem appears as the contribution from the massive bulk extended modes, while the boundary $\eta$ invariant comes entirely from the massless edge-localized modes.Comment: 14 pages, appendices added, details of key equations added, typos corrected, to appear in PTE

Dimethylsulfoxide-quenched hydrogen/deuterium exchange method to study amyloid fibril structure

AbstractA general method to analyze the structure of a supramolecular complex of amyloid fibrils at amino acid residue resolution has been developed. This method combines the NMR-detected hydrogen/deuterium (H/D) exchange technique to detect hydrogen-bonded amide groups and the ability of the aprotic organic solvent dimethylsulfoxide (DMSO) to dissolve amyloid fibrils into NMR-observable, monomeric components while suppressing the undesired H/D exchange reaction. Moreover, this method can be generally applied to amyloid fibrils to elucidate the distribution of hydrogen-bonded amino acid residues in the three-dimensional molecular organization in the amyloid fibrils. In this study, we describe theoretical considerations in the H/D exchange method to obtain the structural information of proteins, and the DMSO-quenched H/D exchange method to study a supramolecular complex of amyloid fibrils. A possible application of this method to study the interaction of a protein/peptide with phospholipid membrane is also discussed