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

Theta vacuum effects on the pseudoscalar condensates and the eta^prime meson in 2-dimensional lattice QED

We study the chiral condensates and the eta^prime meson correlators of the massive Schwinger model in non-zero theta vacuum. Our data suggest that the pseudoscalar operator does condense in a fixed topological sector and gives long range correlations of the eta^prime meson. We find that this is well understood from the clustering decomposition and statistical picture. Our result also indicates that even in theta=0 case, the long range correlation of eta^prime meson receives non-zero contributions from all the topological sectors and that their cancellation is non-trivial and requires accurate measurement of the reweighting factors as well as the expectation values. It is then clear that the fluctuation of the disconnected diagram originates from the pseudoscalar condensates.Comment: Lattice2004(topology), 3pages, 3figure

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

Effects of Z-Isomerization on the Bioavailability and Functionality of Carotenoids: A Review

Carotenoids, the most common fat-soluble plant pigments in nature, are beneficial to human health due to their strong antioxidant activities and abilities to prevent various diseases. Carotenoids have many geometrical isomers forms caused by E/Z-isomerization at arbitrary sites within the multiple conjugated double bonds. Several studies have addressed that the bioavailability as well as the antioxidant, anticancer, and antiatherosclerotic activities of carotenoids varies among the isomers. In addition, those variations differ among carotenoids: Z-isomerization resulted in “positive” or “negative” effect for carotenoids bioavailability and functionality, for example, Z-isomers of lycopene are more bioavailable than the all-E-isomer, whereas the opposite is observed for β-carotene. Thus, to efficiently promote the beneficial effects of carotenoids by ingestion, it is important to have a good understanding of the impact of E/Z-isomerization on the corresponding functional changes. The objective of this contribution is to review the effects of carotenoid Z-isomerization on bioavailability and functionality and describe their differences among carotenoids

Topology conserving gauge action and the overlap-Dirac operator

We apply the topology conserving gauge action proposed by Luescher to the four-dimensional lattice QCD simulation in the quenched approximation. With this gauge action the topological charge is stabilized along the hybrid Monte Carlo updates compared to the standard Wilson gauge action. The quark potential and renormalized coupling constant are in good agreement with the results obtained with the Wilson gauge action. We also investigate the low-lying eigenvalue distribution of the hermitian Wilson-Dirac operator, which is relevant for the construction of the overlap-Dirac operator.Comment: 27pages, 11figures, accepted versio

Salvage restoration after conduit necrosis

In patients with esophageal cancer, esophageal conduit necrosis is a catastrophic complication of esophagectomy that requires surgical restoration. Because such patients are generally fatigued, less-invasive surgery is encouraged whenever possible. Therefore, we trim the sternum minimally above the healthy part of the gastric conduit, expose its surface, and then make anastomoses between the remnant esophagus and the exposed gastric conduit using a free jejunal graft through a retrosternal-subcutaneous route. The risk involved with this procedure is low, because we avoid manipulation of the heavily inflamed lesion due to mediastinitis