Takanori Fujiwara

• Ibaraki University

We study the topological pump for a lattice fermion model mainly in three spatial dimensions. We first calculate the U(1) current density for the Dirac model defined in continuous space-time to review the known results as well as to introduce some technical details convenient for the calculations of the lattice model. We next investigate the U(1) c...

Closed FLRW universe of three-dimensional Einstein gravity with positive cosmological constant in three dimensions is investigated by using the Cillins-Williams formalism in Regge calculus. Spherical Cauchy surface is replaced with regular polyhedrons. The Regge equations are reduced to differential equations in continuum time limit. Numerical solu...

The closed Friedmann--Lema\^itre--Robertson--Walker (FLRW) universe of Einstein gravity with positive cosmological constant in three dimensions is investigated by using the Collins--Williams formalism in Regge calculus. A spherical Cauchy surface is replaced with regular polyhedrons. The Regge equations are reduced to differential equations in the...

We rederive the spectral asymmetry of the Wilson-Dirac model in external fields, paying attention to the Chern number due to the Berry connection. We interpret the smooth part of the spectral asymmetry as the Streda formula which is originally derived for the two-dimensional QHE. We show by numerical calculations that the Streda formula reproduces...

We explore the bulk-edge correspondence for topological insulators (superconductors) without time-reversal symmetry from the point of view of the index theorem for open spaces. We assume generic Hamiltonians not only with a linear dispersion but also with higher order derivatives arising from generic band structures. Using a generalized index theor...

We investigate an index theorem for a Bogoliubov-de Gennes Hamiltonian (BdGH) describing a topological superconductor with Yang-Mills-Higgs couplings in arbitrary dimensions. We find that the index of the BdGH is determined solely by the asymptotic behavior of the Higgs fields and is independent of the gauge fields. It can be nonvanishing if the di...

General framework for quantizing anomalous gauge theories in four dimensions is applied to the description of electroweak theory that lacks the top quark. Auxiliary fields introduced to recover the gauge invariance substitute for the Higgs bosons of the standard model. The gauge invariant action contains the anomaly canceling Wess-Zumino-Witten ter...

We study a Majorana zero-energy state bound to a hedgehog-like point defect in a topological superconductor described by a Bogoliubov-de Gennes (BdG)-Dirac type effective Hamiltonian. We first give an explicit wave function of a Majorana state by solving the BdG equation directly, from which an analytical index can be obtained. Next, by calculating...

Color superconductivity in high density QCD exhibits the color-flavor locked (CFL) phase. To explore zero modes in the CFL phase in the presence of a non-Abelian vortex with an SU(2) symmetry in the vortex core, we apply the index theorem to the Bogoliubov-de Gennes (BdG) Hamiltonian. From the calculation of the topological index, we find that trip...

We propose a Z$_2$ index theorem for a generic topological superconductor in class D. Introducing a particle-hole symmetry breaking term depending on a parameter and regarding it as a coordinate of an extra dimension, we define the index of the zero modes and corresponding topological invariant for such an extended Hamiltonian. It is shown that the...

We derive an index theorem for zero-energy Majorana fermion modes in a superconductor-topological insulator system in both two and three dimensions, which is valid for models with chiral symmetry as well as particle-hole symmetry. For more generic models without chiral symmetry, we suggest that Majorana zero-modes are classified by Z$_2$. Comment:...

With time reversal symmetry a Dirac operator has a vanishing index and a Chern number. We show that we can nevertheless define a nontrivial Z2 index as well as a corresponding topological invariant given by gauge field, which implies that such a Dirac operator is topologically nontrivial.

We present a quantized non-Abelian Berry phase for time reversal invariant systems such as quantum spin Hall effect. Ordinary Berry phase is defined by an integral of Berry's gauge potential along a loop (an integral of the Chern-Simons one-form), whereas we propose that a similar integral but over five dimensional parameter space (an integral of t...

Magnetic translation symmetry on a finite periodic square lattice is investigated for an arbitrary uniform magnetic field in arbitrary dimensions. It can be used to classify eigenvectors of the Hamiltonian. The system can be converted to another system of half or lower dimensions. A higher dimensional generalization of Harper equation is obtained f...

We show that the Z$_2$ invariant, which classifies the topological properties of time reversal invariant insulators, has deep relationship with the global anomaly. Although the second Chern number is the basic topological invariant characterizing time reversal systems, we show that the relative phase between the Kramers doublet reduces the topologi...

We study Dirac operator zero-modes on a torus for gauge background with uniform field strengths. Under the basic translations of the torus coordinates the wave functions are subject to twisted periodic conditions. In suitable torus coordinates the zero-mode wave functions can be related to holomorphic functions of the complex torus coordinates. Hal...

We study Dirac operator zero-modes on a torus for gauge background with uniform field strengths. Under the basic translations of the torus coordinates the wave functions are subject to twisted periodic conditions. In a suitable torus coordinates the zero-mode wave functions can be related to holomorphic functions of the complex torus coordinates. W...

Based upon the lattice Dirac operator satisfying the Ginsparg-Wilson relation, we investigate canonical formulation of massless fermion on the spatial lattice. For free fermion system exact chiral symmetry can be implemented without species doubling. In the presence of gauge couplings the chiral symmetry is violated. We show that the divergence of...

We construct the Wess-Zumino-Witten (WZW) term in lattice gauge theory by using a Dirac operator which obeys the Ginsparg-Wilson relation. Topological properties of the WZW term known in the continuum are reproduced on the lattice as a consequence of a non-trivial topological structure of the space of admissible lattice gauge fields. In the course...

We evaluate for arbitrary even dimensions the classical continuum limit of the lattice axial anomaly defined by the overlap-Dirac operator. Our calculational scheme is simple and systematic. In particular, a powerful topological argument is utilized to determine the value of a lattice integral involved in the calculation. When the Dirac operator is...

The spectral flows of the hermitian Wilson-Dirac operator for a continuous family of abelian gauge fields connecting different topological sectors are shown to have a characteristic structure leading to the lattice index theorem. The index of the overlap Dirac operator is shown to coincide with the topological charge for a wide class of gauge field...

It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An explicit formula for the secular equations is given in term of a set of polynomials. The spectrum exhibits a fractal...

Generic topological structure of the chiral anomalies of lattice U(1) gauge theory in arbitrary dimensions is investigated by applying the BRST cohomological method based on the noncommutative differential calculus.

The chiral anomaly in lattice abelian gauge theory is investigated by applying the geometric and topological method in noncommutative differential geometry(NCDG). A new kind of double complex and descent equation are proposed on infinite hypercubic lattice in arbitrary even dimensional Euclidean space, in the framework of NCDG. Using the general so...

We investigate numerically the spectrum of the hermitian Wilson-Dirac operator in abelian gauge theories on finite lattices. The spectral flows for a continuous family of abelian gauge fields connecting different topological sectors are shown to have a characteristic structure leading to the lattice index theorem. We find that the index of Neuberge...

Block-spin transformations from a fine lattice to a coarse one are shown to give rise to a one-to-one correspondence between the zero-modes of the Ginsparg-Wilson Dirac operator on the fine lattice and those on the coarse lattice. The index is then preserved under the blocking process. Such a one-to-one correspondence is violated and the block-spin...

The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the Ginsparg–Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which m...

The configuration space of abelian gauge theory on a periodic lattice becomes topologically disconnected when exceptional gauge field configurations are removed. It is possible to define a U(1)-bundle from the nonexceptional link variables by a smooth interpolation of the transition functions. The lattice analogue of the Chern character obtained us...

A kind of double complex and a descent equation are proposed on a discrete even-dimensional Euclidean space, i.e. an infinite hyperbolic lattice, in the framework of noncommutative differential geometry (NCDG). Using the general solutions of the proposed descent equation, we derive the chiral anomaly in Abelian lattice gauge theory. The topological...

The chiral anomaly in lattice abelian gauge theory is investigated by applying the geometric and topological method in noncommutative differential geometry(NCDG). A new kind of double complex and descent equation are proposed on infinite hypercubic lattice in arbitrary even dimensional Euclidean space, in the framework of NCDG. Using the general so...

The axial anomaly of lattice abelian gauge theory on a hyper-cubic regular lattice in arbitrary even dimensions is investigated by applying the method of exterior differential calculus. The topological invariance, gauge invariance and locality of the axial anomaly determine the explicit form of the topological part. The anomaly is obtained up to a...

Quantum A2-Toda field theory in two dimensions is investigated based on the method of quantizing canonical free field. Toda exponential operators associated with the fundamental weights are constructed to the fourth order in the cosmological constant. This leads us to a conjecture for the exact operator solution.

Correlation functions of Toda field vertices are investigated by applying the method of integrating zero-mode developed for Liouville theory. We generalize the relations among the zero-, two- and three-point couplings known in Liouville case to arbitrary Toda theories. Two- and three-point functions of Toda vertices associated with the simple roots...

Exact operator solution for quantum Liouville theory is investigated based on the canonical free field. Locality, the field equation and the canonical commutation relations are examined based on the exchange algebra hidden in the theory. The exact solution proposed by Otto and Weigt is shown to be correct to all order in the cosmological constant....

The relation between super-Virasoro anomaly and super-Weyl anomaly in $N=1$ NSR superstring coupled with 2D supergravity is investigated from canonical theoretical view point. The WZW action canceling the super-Virasoro anomaly is explicitly constructed. It is super-Weyl invariant but nonlocal functional of 2D supergravity. The nonlocality can be r...

Two-dimensional supergravity theory is quantized as an anomalous gauge theory. In the Batalin-Fradkin (BF) formalism, the anomaly-canceling super-Liouville fields are introduced to identify the original second-class constrained system with a gauge-fixed version of a first-class system. The BFV-BRST quantization applies to formulate the theory in th...

The relation among the 2D general covariance, the Weyl invariance, the Virasoro anomaly and the trace anomaly in a conformal field theory coupled to 2D gravity is investigated in canonical formalism. A novel Liouville action, which is a local functional of 2D metric fields, is obtained. The quantization in the conformal and the light-cone gauges is...

Based on the extended BRST formalism of Batalin, Fradkin and Vilkovisky, we perform a general algebraic analysis of the BRST anomalies in superstring theory of Neveu-Schwarz-Ramond. Consistency conditions on the BRST anomalies are completely solved. The genuine super-Virasoro anomaly is identified with the essentially unique solution to the consist...

In two-dimensional dilaton gravity theories, there may exist a global Weyl invariance which makes black hole spurious. If the global invariance and the local Weyl invariance of the matter coupling are intact at the quantum level, there is no Hawking radiation. We explicitly verify the absence of anomalies in these symmetries for the model proposed...

Two-dimensional quantum gravity is identified as a second-class system which we convert into a first-class system via the Batalin-Fradkin (BF) procedure. Using the extended phase space method, we then formulate the theory in most general class of gauges. The conformal gauge action suggested by David, Distler and Kawai is derived from a first princi...

The classical 2D cosmological model of Callan, Giddings, Harvey and Strominger possesses a global symmetry that is responsible for decoupling of matter fields. The model is quantized on the basis of the extended phase space method to allow an exhaustive, algebraic analysis to find potential anomalies. Under a certain set of reasonable assumptions w...

Using the generalized hamiltonian method of Batalin, Fradkin and Vilkovisky, we investigate the algebraic structure of anomalies in the Polyakov string theory that appear as the Schwinger terms in super-commutation relations between BRST charge and total hamiltonian. We obtain the most general form of the anomalies in the extended phase space, with...

Anomalous gauge theories considered as constrained systems are investigated. The effects of chiral anomaly on the canonical structure are examined first for nonlinear -model and later for fermionic theory. The breakdown of the Gauss law constraints and the anomalous commutators among them are studied in a systematic way. An intrinsic mass term for...

With the intention of finding a consistent Hamiltonian description of the anomalous nonabelian gauge theories in four dimensions, we examine algebraic properties of the Gauss-law constraints for the chirally gauged nonlinear sigma-model with a Wess-Zumino-Witten term. A relation which, in the Weyl gauge, reduces to Fujikawa's relation ∂0Ga(x) =i(Dµ...

We present a generalized formalism of the hidden local symmetry in which any nonlinear sigma model based on the manifold G/H is gauge equivalent to a model possessing G_{mathrm{global}} x G_{mathrm{local}} symmetry, which is a natural extension of the well-known gauge equivalence between a G/H nonlinear sigma model and a G_{mathrm{global}} x H_{mat...

Using canonical operator formalism, the chiral U(1) anomalies are investigated in model field theories with 1+1 dimensions. In some special cases, these theories have those particle spectra which behave effectively as two dimensional Weyl fields. This must be taken into account in defining charge operators with normal ordering. It is shown how such...

An effective lagrangian is constructed for the system of pions, ρ mesons and skyrmions in the light of a hidden local SU(2) symmetry in a non-linear sigma model. It describes vector dominance relations such as the KSRF relation, the ρ universality and the ρ-pole dominance in the photon coupling. It also satisfies all soft-pion threshold theorems.

Using the idea of cohomology defined for the Lie algebra of gauge transformations, we examine the extension of the current algebra for the system of the gauged nonlinear sigma-model. An anomalous term in the current commutation relation is constructed and shown to be equivalent to that arising in the gauged nonlinear sigma-model with the Wess-Zumin...

We present general solutions to the Wess-Zumino anomaly equation which incorporate vector mesons as dynamical gauge bosons of the hidden local symmetry in the nonlinear chiral Lagrangian. In contrast to the previous attempts to introduce the vector mesons, our formalism enables one to treat consistently and systematically various processes associat...

A nontrivial extension of current algebra is investigated using the techniques of differential geometry. The condition for the extension is derived. It is shown that a nontrivial solution leads to field equations with the Wess-Zumino-Witten anomaly. A simple application of the scheme to Yang-Mills gauge theory is discussed also. I would like to tha...