Junya Yagi
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Junya Yagi has a total of 17 co-authors. Here are the top co-authors by number of shared publications:
- Kazunobu Maruyoshi
Seikei University
4 shared publications - Meng-Chwan Tan
Department of Physics National University of Singapore 2 Science Drive 3 117551 Singapore
4 shared publications - Yuan Luo
National University of Singapore
4 shared publications - Atsuo Kuniba
Institute of Physics Graduate School of Arts and Sciences University of Tokyo 153-8902 Komaba Tokyo Japan
2 shared publications - Kevin Costello
Perimeter Institute for Theoretical Physics
2 shared publications - Qin Zhao
Department of Physics National University of Singapore 2 Science Drive 3 117551 Singapore
2 shared publications
Latest Publications
- 30 June 2026
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 59 (28) , 285203
State integral models and the tetrahedron equation
It is shown that for a class of state integral models on shaped pseudo 3-manifolds, including the edge formulation of Teichmüller TQFT, the Boltzmann weight assigned to a tetrahedron solves the tetrahedron equation. The dihedral angles of the tetrahedron play the role of spectral parameters.
- 30 June 2026
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 59 (28) , 285203
State integral models and the tetrahedron equation
It is shown that for a class of state integral models on shaped pseudo 3-manifolds, including the edge formulation of Teichmüller TQFT, the Boltzmann weight assigned to a tetrahedron solves the tetrahedron equation. The dihedral angles of the tetrahedron play the role of spectral parameters.
- Open Access
- 12 June 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (6)
Solving the tetrahedron equation by Teichmüller TQFT
A bstract: We propose an approach to construct three-dimensional lattice models using line defects in state integral models on shaped triangulations of 3-manifolds. The Boltzmann weights for these models satisfy a variant of the tetrahedron equation, which implies integrability under suitable assumptions on R-matrices and transfer matrices. As an explicit example, we present a solution produced by Teichmüller TQFT.
- 12 June 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (6)
Open AccessSolving the tetrahedron equation by Teichmüller TQFT
A bstract: We propose an approach to construct three-dimensional lattice models using line defects in state integral models on shaped triangulations of 3-manifolds. The Boltzmann weights for these models satisfy a variant of the tetrahedron equation, which implies integrability under suitable assumptions on R-matrices and transfer matrices. As an explicit example, we present a solution produced by Teichmüller TQFT.
- Open Access
Quantized six-vertex model on a torus
We study the integrability of the quantized six-vertex model with four parameters on a torus. It is a three-dimensional integrable lattice model in which a layer transfer matrix, depending on two spectral parameters associated with the homology cycles of the torus, can be defined not only on the square lattice but also on more general graphs. For a class of graphs that we call admissible, we establish the commutativity of the layer transfer matrices by introducing four types of tetrahedron equations and two types of inversion relations. Expanding in the spectral parameters yields a family of commuting quantum Hamiltonians. The quantized six-vertex model can also be reformulated in terms of (quantized) dimer models, and encompasses known integrable systems as special cases, including the free parafermion model and the relativistic Toda chain.
Open AccessQuantized six-vertex model on a torus
We study the integrability of the quantized six-vertex model with four parameters on a torus. It is a three-dimensional integrable lattice model in which a layer transfer matrix, depending on two spectral parameters associated with the homology cycles of the torus, can be defined not only on the square lattice but also on more general graphs. For a class of graphs that we call admissible, we establish the commutativity of the layer transfer matrices by introducing four types of tetrahedron equations and two types of inversion relations. Expanding in the spectral parameters yields a family of commuting quantum Hamiltonians. The quantized six-vertex model can also be reformulated in terms of (quantized) dimer models, and encompasses known integrable systems as special cases, including the free parafermion model and the relativistic Toda chain.
- Open Access
- 21 December 2024
- Published by SIGMA (Symmetry, Integrability and Geometry: Methods and Application) in Symmetry, Integrability and Geometry: Methods and Applications
- Vol. 20, 113
Solutions of Tetrahedron Equation from Quantum Cluster Algebra Associated with Symmetric Butterfly Quiver
We construct a new solution to the tetrahedron equation by further pursuing the quantum cluster algebra approach in our previous works. The key ingredients include a symmetric butterfly quiver attached to the wiring diagrams for the longest element of type $A$ Weyl groups and the implementation of quantum $Y$-variables through the $q$-Weyl algebra. The solution consists of four products of quantum dilogarithms. By exploring both the coordinate and momentum representations, along with their modular double counterparts, our solution encompasses various known three-dimensional (3D) $R$-matrices. These include those obtained by Kapranov-Voevodsky (1994) utilizing the quantized coordinate ring, Bazhanov-Mangazeev-Sergeev (2010) from a quantum geometry perspective, Kuniba-Matsuike-Yoneyama (2023) linked with the quantized six-vertex model, and Inoue-Kuniba-Terashima (2023) associated with the Fock-Goncharov quiver. The 3D $R$-matrix presented in this paper offers a unified perspective on these existing solutions, coalescing them within the framework of quantum cluster algebra.- 21 December 2024
- Published by SIGMA (Symmetry, Integrability and Geometry: Methods and Application) in Symmetry, Integrability and Geometry: Methods and Applications
- Vol. 20, 113
Open AccessSolutions of Tetrahedron Equation from Quantum Cluster Algebra Associated with Symmetric Butterfly Quiver
We construct a new solution to the tetrahedron equation by further pursuing the quantum cluster algebra approach in our previous works. The key ingredients include a symmetric butterfly quiver attached to the wiring diagrams for the longest element of type $A$ Weyl groups and the implementation of quantum $Y$-variables through the $q$-Weyl algebra. The solution consists of four products of quantum dilogarithms. By exploring both the coordinate and momentum representations, along with their modular double counterparts, our solution encompasses various known three-dimensional (3D) $R$-matrices. These include those obtained by Kapranov-Voevodsky (1994) utilizing the quantized coordinate ring, Bazhanov-Mangazeev-Sergeev (2010) from a quantum geometry perspective, Kuniba-Matsuike-Yoneyama (2023) linked with the quantized six-vertex model, and Inoue-Kuniba-Terashima (2023) associated with the Fock-Goncharov quiver. The 3D $R$-matrix presented in this paper offers a unified perspective on these existing solutions, coalescing them within the framework of quantum cluster algebra. - Top Cited PapersOpen Access
- 5 November 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (11) , 1-76
Q-operators are ’t Hooft lines
We study ’t Hooft lines in four-dimensional holomorphic-topological Chern-Simons theory. We relate them to Q-operators in the theory of integrable systems. We give a physical interpretation of the fundamental TQ and QQ relations satisfied by Q-operators and conventional transfer matrices.
- 5 November 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (11) , 1-76
Top Cited PapersOpen AccessQ-operators are ’t Hooft lines
We study ’t Hooft lines in four-dimensional holomorphic-topological Chern-Simons theory. We relate them to Q-operators in the theory of integrable systems. We give a physical interpretation of the fundamental TQ and QQ relations satisfied by Q-operators and conventional transfer matrices.
- Open Access
- 5 August 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (8) , 1-25
Tetrahedron duality
A bstract: A certain two-dimensional supersymmetric gauge theory is argued to satisfy a relation that promotes the Zamolodchikov tetrahedron equation to an infrared duality between two quantum field theories. Solutions of the tetrahedron equation with continuous spin variables are obtained from partition functions of this theory and its variants.
- 5 August 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (8) , 1-25
Open AccessTetrahedron duality
A bstract: A certain two-dimensional supersymmetric gauge theory is argued to satisfy a relation that promotes the Zamolodchikov tetrahedron equation to an infrared duality between two quantum field theories. Solutions of the tetrahedron equation with continuous spin variables are obtained from partition functions of this theory and its variants.
- Open Access
- 9 January 2023
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2023 (1) , 1-38
Integrable 3D lattice model in M-theory
- 9 January 2023
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2023 (1) , 1-38
Open AccessIntegrable 3D lattice model in M-theory
- Open Access
Cluster transformations, the tetrahedron equation and three-dimensional gauge theories
We define three families of quivers in which the braid relations of the symmetric group $S_n$ are realized by mutations and automorphisms. A sequence of eight braid moves on a reduced word for the longest element of $S_4$ yields three trivial cluster transformations with 8, 32 and 32 mutations. For each of these cluster transformations, a unitary operator representing a single braid move in a quantum mechanical system solves the tetrahedron equation. The solutions thus obtained are constructed from the noncompact quantum dilogarithm and can be identified with the partition functions of three-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories on a squashed three-sphere.Open AccessCluster transformations, the tetrahedron equation and three-dimensional gauge theories
We define three families of quivers in which the braid relations of the symmetric group $S_n$ are realized by mutations and automorphisms. A sequence of eight braid moves on a reduced word for the longest element of $S_4$ yields three trivial cluster transformations with 8, 32 and 32 mutations. For each of these cluster transformations, a unitary operator representing a single braid move in a quantum mechanical system solves the tetrahedron equation. The solutions thus obtained are constructed from the noncompact quantum dilogarithm and can be identified with the partition functions of three-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories on a squashed three-sphere. - Open Access
Wilson-'t Hooft lines as transfer matrices
We establish a correspondence between a class of Wilson-'t Hooft lines in four-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-'t Hooft lines in a twisted product space $S^1 \times_\epsilon \mathbb{R}^2 \times \mathbb{R}$ by supersymmetric localization and show that they are equal to the Wigner transforms of the transfer matrices. A variant of the AGT correspondence implies an identification of the transfer matrices with Verlinde operators in Toda theory, which we also verify. We explain how these field theory setups are related to four-dimensional Chern-Simons theory via embedding into string theory and dualities.Open AccessWilson-'t Hooft lines as transfer matrices
We establish a correspondence between a class of Wilson-'t Hooft lines in four-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-'t Hooft lines in a twisted product space $S^1 \times_\epsilon \mathbb{R}^2 \times \mathbb{R}$ by supersymmetric localization and show that they are equal to the Wigner transforms of the transfer matrices. A variant of the AGT correspondence implies an identification of the transfer matrices with Verlinde operators in Toda theory, which we also verify. We explain how these field theory setups are related to four-dimensional Chern-Simons theory via embedding into string theory and dualities. - Open Access
- 13 January 2021
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2021 (1) , 1-31
Wilson-’t Hooft lines as transfer matrices
We establish a correspondence between a class of Wilson-’t Hooft lines in four-dimensional $$ \mathcal{N} $$ = 2 supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-’t Hooft lines in a twisted product spaceS1×ϵℝ2× ℝ by supersymmetric localization and show that they are equal to the Wigner transforms of the transfer matrices. A variant of the AGT correspondence implies an identification of the transfer matrices with Verlinde operators in Toda theory, which we also verify. We explain how these field theory setups are related to four-dimensional Chern-Simons theory via embedding into string theory and dualities.- 13 January 2021
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2021 (1) , 1-31
Open AccessWilson-’t Hooft lines as transfer matrices
We establish a correspondence between a class of Wilson-’t Hooft lines in four-dimensional $$ \mathcal{N} $$ = 2 supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-’t Hooft lines in a twisted product spaceS1×ϵℝ2× ℝ by supersymmetric localization and show that they are equal to the Wigner transforms of the transfer matrices. A variant of the AGT correspondence implies an identification of the transfer matrices with Verlinde operators in Toda theory, which we also verify. We explain how these field theory setups are related to four-dimensional Chern-Simons theory via embedding into string theory and dualities.