25 citations · 35 across the 15 of their papers we have counts for
16 papers
The index of mesoscopic Wilson--Dirac operators: I
Mikio Furuta, Shinichiroh Matsuo
This is the first of a series of papers which will be devoted to a study of the index of mesoscopic Wilson--Dirac operators on closed Riemannian manifolds. The aim of the series is…
Generalization of lattice Dirac operator index
Shoto Aoki, Hajime Fujita, Hidenori Fukaya +4
We provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing -theory to classify the Wilson Dirac operator via its spectral flow. In…
Capturing the Atiyah-Patodi-Singer index from the lattice
Shoto Aoki, Hajime Fujita, Hidenori Fukaya +4
We construct a formulation of the Atiyah-Patodi-Singer index of Dirac operators in lattice gauge theory for domains with compact boundaries in a flat torus. The key idea is to expl…
-theoretic computation of the Atiyah(-Patodi)-Singer index of lattice Dirac operators
Shoto Aoki, Hidenori Fukaya, Mikio Furuta +3
We show that the Wilson Dirac operator in lattice gauge theory can be identified as a mathematical object in -theory and that its associated spectral flow is equal to the index.…
invariant of massive Wilson Dirac operator and the index
Shoto Aoki, Hidenori Fukaya, Mikio Furuta +3
We revisit the lattice index theorem in the perspective of -theory. The standard definition given by the overlap Dirac operator equals to the invariant of the Wilson Dirac o…
The index of lattice Dirac operators and -theory
Shoto Aoki, Hidenori Fukaya, Mikio Furuta +3
We mathematically show an equality between the index of a Dirac operator on a flat continuum torus and the invariant of a lattice Dirac operator known as the Wilson Dirac opera…
A physicist-friendly reformulation of the mod-two Atiyah-Patodi-Singer index
Hidenori Fukaya, Mikio Furuta, Yoshiyuki Matsuki +4
Gauge anomaly in 4-dimensions can be viewed as a current inflow into an extra-dimension, where the total phase of the fermion partition function is given in a gauge invariant way b…
Mod-two APS index and domain-wall fermion
Hidenori Fukaya, Mikio Furuta, Yoshiyuki Matsuki +4
We reformulate the mod-two Atiyah-Patodi-Singer (APS) index in a physicist-friendly way using the domain-wall fermion. Our new formulation is given on a closed manifold, which is e…
A physicist-friendly reformulation of the Atiyah-Patodi-Singer index and its mathematical justification
Hidenori Fukaya, Mikio Furuta, Shinichiroh Matsuo +3
The Atiyah-Patodi-Singer index theorem describes the bulk-edge correspondence of symmetry protected topological insulators. The mathematical setup for this theorem is, however, not…
The Atiyah-Patodi-Singer index and domain-wall fermion Dirac operators
Hidenori Fukaya, Mikio Furuta, Shinichiroh Matsuo +3
We introduce a mathematician-friendly formulation of the physicist-friendly derivation of the Atiyah-Patodi-Singer index of our previous paper. Our viewpoint sheds some new light o…
Yamabe Invariants and the -monopole Equations
Masashi Ishida, Shinichiroh Matsuo, Nobuhiro Nakamura
We compute the Yamabe invariants for a new infinite class of closed -dimensional manifolds by using a "twisted" version of the Seiberg-Witten equations, the -…
The perturbation of the Seiberg-Witten equations revisited
Mikio Furuta, Shinichiroh Matsuo
We introduce a new class of perturbations of the Seiberg-Witten equations. Our perturbations offer flexibility in the way the Seiberg-Witten invariants are constructed and also she…
The prescribed scalar curvature problem for metrics with unit total volume
Shinichiroh Matsuo
We solve the modified Kazdan-Warner problem of finding metrics with prescribed scalar curvature and unit total volume.
Local mean dimension of ASD moduli spaces over the cylinder
Shinichiroh Matsuo, Masaki Tsukamoto
We study an infinite dimensional ASD moduli space over the cylinder. Our main result is the formula of its local mean dimension. A key ingredient of the argument is the notion of n…
Brody curves and mean dimension
Shinichiroh Matsuo, Masaki Tsukamoto
We study the mean dimensions of the spaces of Brody curves. In particular we give the formula of the mean dimension of the space of Brody curves in the Riemann sphere.
Instanton approximation, periodic ASD connections, and mean dimension
Shinichiroh Matsuo, Masaki Tsukamoto
We study a moduli space of ASD connections over . We consider not only finite energy ASD connections but also infinite energy ones. So the moduli space is inf…