48 citations · 135 across the 22 of their papers we have counts for
22 papers
Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation
Shoto Aoki, Yoshio Kikukawa, Toshinari Takemoto
We study the duality structure of lattice Maxwell theory with a theta term in the Hamiltonian Villain formulation. Reflecting the fact that odd-level Chern--Simons theory depends o…
Exact SL(2,Z)-Structure of Lattice Maxwell Theory with -term in Modified Villain Formulation
Shoto Aoki, Yoshio Kikukawa, Toshinari Takemoto
We study the duality of lattice Maxwell theory in the modified Villain formulation, employing an ultra-local action with a theta term. Although this action is known to become non u…
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…
Chiral Anomaly of Kogut-Susskind Fermion in the (3+1)-dimensional Hamiltonian formalism
Shoto Aoki, Yoshio Kikukawa, Toshinari Takemoto
We consider Kogut-Susskind fermions (also known as staggered fermions) in a -dimensional Hamiltonian formalism and examine a chiral transformation and its associated chiral…
-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.…
Lattice Weyl Fermion on a Single Spherical Domain-Wall
Shoto Aoki, Hidenori Fukaya, Naoto Kan
We investigate a single spherical domain-wall embedded in a three-dimensional Euclidean lattice. We employ the Shamir-type domain-wall fermion formulation, where the negative mass…
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…
Computation of the index on orbifold from the Atiyah-Segal-Singer fixed point theorem
Shoto Aoki, Maki Takeuchi
We investigate the independent chiral zero modes on the orbifolds from the Atiyah-Segal-Singer fixed point theorem. The required information for this calculation includes the fixed…
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…
Study of Curved Domain-wall Fermions on a Lattice
Shoto Aoki
In this thesis, we consider fermion systems on square lattice spaces with a curved domain-wall mass term. In a similar way to the flat case, we find massless and chiral states loca…
A lattice regularization of Weyl fermions in a gravitational background
Shoto Aoki, Hidenori Fukaya, Naoto Kan
We report on a lattice fermion formulation with a curved domain-wall mass term to nonperturbatively describe fermions in a gravitational background. In our previous work in 2022, w…
A lattice formulation of Weyl fermions on a single curved surface
Shoto Aoki, Hidenori Fukaya, Naoto Kan
In the standard lattice domain-wall fermion formulation, one needs two flat domain-walls where both of the left- and right-handed massless modes appear. In this work we investigate…
A Microscopic study of Magnetic monopoles in Topological Insulators
Shoto Aoki, Hidenori Fukaya, Naoto Kan +2
In this article, we analyze a magnetic monopole in topological insulators. The monopole obtain a fractional electric charge because of the Witten effect. We consider this system wi…
Why magnetic monopole becomes dyon in topological insulators
Shoto Aoki, Hidenori Fukaya, Naoto Kan +2
The Witten effect predicts that a magnetic monopole acquires a fractional electric charge inside topological insulators. In this work, we give a microscopic description of this phe…
Curved domain-wall fermion and its anomaly inflow
Shoto Aoki, Hidenori Fukaya
We investigate the effect of gauge field on lattice fermion systems with a curved domain-wall mass term. In the same way as the conventional flat domain-wall fermion, the c…
Curved domain-wall fermions
Shoto Aoki, Hidenori Fukaya
We consider fermion systems on a square lattice with a mass term having a curved domain-wall. Similarly to the conventional flat domain-wall fermions, massless and chiral edge stat…
Chiral fermion on curved domain-wall
Shoto Aoki, Hidenori Fukaya
We consider a massive fermion system having a curved domain-wall embedded in a square lattice. In a similar way to the conventional flat domain-wall fermion, chiral massless modes…
Algebra of Hyperbolic Band Theory under Magnetic Field
Kazuki Ikeda, Yoshiyuki Matsuki, Shoto Aoki
We explore algebras associated with the hyperbolic band theory under a magnetic field for the first time. We define the magnetic Fuchsian group associated with a higher genus Riema…
Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface
Kazuki Ikeda, Shoto Aoki, Yoshiyuki Matsuki
We explore the hyperbolic band theory under a magnetic field for the first time. Our theory is a general extension of the conventional band theory defined on a Euclidean lattice in…
Theory of Quantum Games and Quantum Economic Behavior
Kazuki Ikeda, Shoto Aoki
The quest of this work is to present discussions of some fundamental questions of economics in the era of quantum technology, which require a treatment different from economics stu…
Infinitely Repeated Quantum Games and Strategic Efficiency
Kazuki Ikeda, Shoto Aoki
Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at mo…