arXiv subjects

Hayato Kanno

Publications and source records attributed to Hayato Kanno.

7 recordsLinked to original sources

arXiv2026

The $\mathfrak{sl}_2$-algebra structure of multiple Eisenstein series

We prove that the algebra of multiple Eisenstein series is an $\mathfrak{sl}_2$-algebra. In particular, we show that it is graded by weight, which also holds after taking complex linear spans. Further, we identify it as a graded $\mathbb{Q}$-algebra with the associated graded algebra of $q$-analogues of multiple zeta values with respect to the weight filtration. The main ingredient is an estimate that compares the usual defining sums of multiple Eisenstein series with sums over a lattice order depending on an integer $N$.

math.NT↗

arXiv2026

Relations and Derivatives of Multiple Eisenstein Series

In this paper, we study multiple Eisenstein series, which build a natural bridge between the theory of multiple zeta values and modular forms. We prove a large family of relations among these series and give an explicit formula for their derivatives. This formula is expressed using the double shuffle structure and the Drop1 operator introduced by Hirose, Maesaka, Seki, and Watanabe. In particular, the space of multiple Eisenstein series is closed under the derivative. Further we construct bi-multiple Eisenstein series, which give a realization of the formal multiple Eisenstein series as holomorphic functions on the upper half-plane, and we prove a conjecture of Okounkov on derivatives of $q$-analogues of multiple zeta values. Based on the derivative formula, we propose a family of linear relations that is conjectured to generate all linear relations among multiple Eisenstein series. Motivated by this conjecture, we introduce a space of formal multiple Eisenstein series and show that it is an $\mathfrak{sl}_2$-algebra.

math.NT↗

arXiv2025

Grassmann tensor renormalization group for the massive Schwinger model with a $θ$ term using staggered fermions

We use the Grassmann tensor renormalization group method to investigate the $N_f=2$ Schwinger model with the staggered fermions in the presence of a $2π$ periodic $θ$ term in a broad range of mass. The method allows us to deal with the massive staggered fermions straightforwardly and to study the $θ$ dependence of the free energy and topological charge in the thermodynamic limit. Our calculation provides consistent results with not only the analytical solution in the large mass limit but also the previous Monte Carlo studies in the small mass regime. Our numerical results also suggest that the $N_f=2$ Schwinger model on a lattice has a different phase structure, than the model in the continuum limit.

hep-lat↗

arXiv2025

Multiple $\wp$-Functions and Their Applications

In this paper, we introduce and study multiple $\wp$-functions, which generalize the classical Weierstrass $\wp$-function to iterated sums over lattice points, and we establish explicit formulas expressing them in terms of single $\wp$-functions with coefficients given by multiple Eisenstein series. As an application, we derive some relations among multiple Eisenstein series and multiple zeta values by exploiting the double periodicity of the multiple $\wp$-functions.

math.NT↗

arXiv2025

Shuffle regularization for multiple Eisenstein series of level $N$

Bachmann and Tasaka discovered a relationship between multiple Eisenstein series (MES) of level 1 and formal iterated integrals corresponding to multiple zeta value. They also constructed shuffle regularized MES of level 1, which satisfies the shuffle relation that is same as multiple zeta values. In this paper, we expand their results for arbitrary level and give some linear relations among MES of level $N$.

math.NT↗

arXiv2025

Grassmann Tensor Renormalization Group for two-flavor massive Schwinger model with a theta term

We investigate the $N_f=2$ Schwinger model with the massive staggered fermions in the presence of a $2π$ periodic $θ$ term, using the Grassmann tensor renormalization group. Thanks to the Grassmann tensor network formulation, there is no difficulty in dealing with the massive staggered fermions. We study the $θ$ dependence of the free energy in the thermodynamic limit. Our calculation provides consistent results with the analytical solution in the large mass limit. The results also suggest that the $N_f=2$ Schwinger model on a lattice has a different phase structure from that described by the continuum theory.

hep-lat↗

arXiv2021

Anomaly and Superconnection

We study anomalies of fermions with spacetime dependent mass. Using Fujikawa's method, it is found that the anomalies associated with the $U(N)_+\times U(N)_-$ chiral symmetry and $U(N)$ flavor symmetry for even and odd dimensions, respectively, can be written in terms of superconnections. In particular, the anomaly for a vector-like $U(1)$ symmetry is given by the Chern character of the superconnection in both even and odd dimensional cases. It is also argued that the non-Abelian anomaly for a system in D-dimensional spacetime is characterized by a (D+2)-form part of the Chern character of the superconnection which generalizes the usual anomaly polynomial for the massless case. These results enable us to analyze anomalies in the systems with interfaces and spacetime boundaries in a unified way. Applications to index theorems, including Atiyah-Patodi-Singer index theorem and Callias-type index theorem, are also discussed. In addition, we give a natural string theory interpretation of these results.

hep-th↗