arXiv subjects

Tatsuya Yamaoka

Publications and source records attributed to Tatsuya Yamaoka.

8 recordsLinked to original sources

arXiv2026

Taste-splitting mass and edge modes in $3+1$ D staggered fermions

We investigate the symmetry structure of the $3+1$ D staggered fermion Hamiltonian and its implications for anomalies. Since the spin and flavor degrees of freedom of Dirac fermions are distributed over the lattice, in addition to the standard on-site mass term, the staggered fermion system also admits one-, two-, and three-link bilinear terms within a unit cube as local, charge conserving mass terms with different spin and flavor dependence. We identify the spin flavor structures of all those bilinear mass terms and determine the symmetries preserved by each of them. Among them, one of the one-link mass terms preserves a larger residual symmetry associated with conserved charges that generate the Onsager algebra. Motivated by this structure, we consider a kink profile of the one-link mass and analyze the resulting domain-wall system. In the low-energy limit, the $3+1$ D bulk becomes gapped, while two-flavor massless Dirac fermions appear as localized modes on the $2+1$ D domain wall. We show that the bulk conserved charges act on the wall as generators of a flavor $\mathrm{SU}(2)$ symmetry, and that no symmetric mass gap is allowed for the boundary theory when this $\mathrm{SU}(2)$ symmetry and space reflection symmetry are both imposed. This realizes the parity anomaly of the boundary theory and shows that the boundary flavor symmetry and anomaly descend from the ultraviolet staggered-fermion Hamiltonian rather than emerging only in the infrared.

hep-lat↗

arXiv2026

Conserved Non-Singlet Charges for Staggered Fermion Hamiltonian in 3+1 Dimensions

We study conserved charges of the staggered fermion Hamiltonian in 3+1 dimensions. By decomposing staggered fermions into Majorana components and exploiting lattice translation symmetries, we construct a set of conserved non-singlet charges. We analyze their algebra andshow that, although the charges exhibit nontrivial non-commutativity on the lattice, they generate axial SU(2)_L \tines SU(2)_R transformations for low-energy degrees of freedom in the continuum limit. Possible implications for anomalies are discussed.

hep-lat↗

arXiv2026

The Axial Charge in Hilbert Space and the Role in Chiral Gauge Theories

We investigate the Hamiltonian formulation of 1+1-dimensional staggered fermions and reconstruct the vector and axial charge operators, originally identified by Arkya Chatterjee et al., within the Wilson fermion formalism. These operators commute with the Hamiltonian and reduce, in the continuum limit, to the generators of the vector and axial $\mathrm{U}(1)$ symmetries. A notable feature of the axial charge operator is that it acts locally on operators and possesses quantized eigenvalues. Its eigenstates can therefore be interpreted as fermion states with well-defined integer chirality, analogous to those in the continuum theory. This structure enables the formulation of a gauge theory in which the axial $\mathrm{U}(1)_A$ symmetry is promoted to a gauge symmetry. We construct a Hamiltonian in terms of the eigenstates of the axial charge operator, thereby preserving exact axial symmetry on the lattice while recovering vector symmetry in the continuum limit. As applications, we study the implementation of the Symmetric Mass Generation (SMG) mechanism in the 3-4-5-0 models. Our framework admits symmetry-preserving interaction terms with quantized chiral charges, although further numerical investigation is required to confirm the realization of the SMG mechanism in interacting systems.

hep-lat↗

arXiv2025

Non-singlet conserved charges and anomalies in 3+1 D staggered fermions

In this paper, we show that the 3+1 D staggered fermion Hamiltonian possesses, in addition to the conserved charge $Q_0$ that generates the vector $\mathrm{U}(1)_V$ transformation, conserved charges $Q_F$ that generate the $\mathrm{SU}(2)_A$ transformations in the continuum limit, acting simultaneously on left- and right-handed Weyl fermions in opposite directions. Each conserved charge $Q_F$ can be regarded as the generator of a $\mathrm{U}(1)_F$ subgroup of $\mathrm{SU}(2)_L \times \mathrm{SU}(2)_R \times \mathrm{U}(1)_A$. One of these lattice charges satisfies the Onsager algebra. On the lattice, the charges $Q_F$ do not commute with $Q_0$, and no symmetric mass term exists that commutes with both $Q_0$ and $Q_F$. This signals the presence of a mixed anomaly. Remarkably, however, in the continuum limit, a symmetric mass term commuting with both $Q_0$ and $Q_F$ can be constructed. % This implies that the non-trivial lattice anomaly becomes a trivial anomaly in the continuum QFT. This means that the mixed anomaly that is nontrivial on the lattice becomes trivial in the IR QFT obtained in the continuum limit, which is consistent with the analysis of the Ward--Takahashi (WT) identity on the lattice. Indeed, by evaluating this identity associated with the $\mathrm{U}(1)_F$ transformation on the lattice, we confirm that $\mathrm{U}(1)_F$ symmetry is exactly conserved.

hep-lat↗

arXiv2025

Quantized Axial Charge in the Hamiltonian Approach to Wilson Fermions

We investigate the Hamiltonian formulation of 1+1~D staggered fermions and reconstruct vector and axial charge operators, found by Arkya Chatterjee et al., using the Wilson fermion formalism. These operators commute with the Hamiltonian and become the generators of vector and axial $\mathrm{U}(1)$ symmetries in the continuum limit. An interesting feature of the axial charge operator is that it acts locally on operators and has quantized eigenvalues in momentum space. Therefore, the eigenstates of this operator can be interpreted as fermion states with a well-defined integer chirality, analogous to those in the continuum theory. This allows us to realize a gauge theory where the axial $\mathrm{U}(1)_A$ symmetry acts as a gauge symmetry. We construct a Hamiltonian using the eigenstates of the axial charge operator, preserving exact axial symmetry on the lattice and vector symmetry in the continuum. As applications, we examine the implementation of the Symmetric Mass Generation (SMG) mechanism in the $1^4(-1)^4$ and 3-4-5-0 models. Our formulation supports symmetry-preserving interactions with quantized chiral charges, although further numerical studies are required to verify the SMG mechanism in interacting models.

hep-lat↗

arXiv2025

Discrete symmetry and 't Hooft anomalies for 3450 model

We report our study of the discrete symmetry for lattice 3450 model proposed by Wang and Wen. Lattice 3450 model is expected to describe the anomaly free chiral U(1) gauge theory in 1+1 dimension using 2+1 dimensional domain-wall fermion with gapping interactions for the mirror sector. We find that the lattice model has exact discrete symmetry in addition to U(1) x U(1) symmetry. Assuming the Zumino-Stora procedure works also for discrete symmetry, we compute the full 't Hooft anomaly for the target continuum U(1) chiral gauge theory with the same discrete symmetry. We show that the mixed and self anomalies involving the discrete symmetry are absent, which is consistent with the expectation that the lattice 3450 produces chiral U(1) gauge theory in the continuum limit.

hep-lat↗

arXiv2025

SU(6) model revisited

We discuss the vacuum structure of the SU(6) model, a chiral gauge theory, from the perspective of anomaly matching. To this end, we first identify all possible 't Hooft anomalies in the UV theory using the Stora-Zumino procedure. Subsequently, we construct an effective theory by applying the idea of the Wess-Zumino-Witten action to derive the topological terms that encode the 't Hooft anomalies. As a result, we demonstrate that a low-energy effective theory reproducing one of the anomalies, namely the mixed anomaly, is described by a Z3-valued scalar field. On the other hand, the effective theory that accounts for the discrete chiral self-anomaly is significantly more intricate, and elucidating its structure remains an ongoing challenge.

hep-lat↗

arXiv2023

Energies and a gravitational charge for massive particles in general relativity

In this paper, we investigate relations or differences among various conserved quantities which involve the matter Energy Momentum Tensor (EMT) in general relativity. These charges include the energy with Einstein's pseudo EMT, the generalized Komar integral, or the ADM energy, all of which can be derived from Noether's second theorem, as well as an extra conserved charge recently proposed in general relativity. For detailed analyses, we apply definitions of these charges to a system of free massive particles. We employ the post-Newtonian (PN) expansion to make physical interpretations. We find that the generalized Komar integral is not conserved at the first non-trivial order in the PN expansion due to non-zero contributions at spatial boundaries, while the energy with Einstein's pseudo EMT at this order agrees with a total energy of massive particles with gravitational interactions through the Newtonian potential, and thus is conserved. In addition, this total energy is shown to be identical to the ADM energy not only at this order but also all orders in the PN expansion. We next calculate an extra conserved charge for the system of massive particles, at all orders in the PN expansion, which turns out to be a total number of particles. We call it a gravitational charge, since it is clearly different from the total energy. We finally discuss an implication from a fact that there exist two conserved quantities, energy and gravitational charge, in general relativity.

gr-qc↗