English
Related papers

Related papers: Boundary from bulk integrability in three dimensio…

200 papers

We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the…

Strongly Correlated Electrons · Physics 2018-02-01 Iris Cong , Meng Cheng , Zhenghan Wang

This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…

Analysis of PDEs · Mathematics 2021-06-25 Philippe Laurent , Guillaume Legendre , Julien Salomon

Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…

Numerical Analysis · Mathematics 2020-07-20 Heping Dong , Jun Lai , Peijun Li

We construct the boundary algebraic Bethe Ansatz for the AdS3 X S3 X T4 integrable reflection problem restricted to the massless sector. We derive the double-row monodromy and find the appropriate formulation of the dual equation of…

High Energy Physics - Theory · Physics 2024-12-02 Daniele Bielli , Vasileios Moustakis , Alessandro Torrielli

We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in three dimensions. The coupling is realized with a mortar…

Numerical Analysis · Mathematics 2024-07-25 Christoph Erath , Lorenzo Mascotto , Jens Markus Melenk , Ilaria Perugia , Alexander Rieder

We use the numerical conformal bootstrap to study boundary quantum electrodynamics, the theory of a four dimensional photon in a half space coupled to charged conformal matter on the boundary. This system is believed to be a boundary…

High Energy Physics - Theory · Physics 2023-12-14 Samuel Bartlett-Tisdall , Christopher P. Herzog , Vladimir Schaub

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…

High Energy Physics - Theory · Physics 2024-08-06 Junya Yagi

The recent article [arXiv:2307.12552] gave local topological order (LTO) axioms for a quantum spin system, showed they held in Kitaev's Toric Code and in Levin-Wen string net models, and gave a bulk boundary correspondence to describe bulk…

Strongly Correlated Electrons · Physics 2023-09-26 Mario Tomba , Shuqi Wei , Brett Hungar , Daniel Wallick , Kyle Kawagoe , Chian Yeong Chuah , David Penneys

From the q-oscillator solution to the tetrahedron equation associated with a quantized coordinate ring, we construct solutions to the Yang-Baxter equation by applying a reduction procedure formulated earlier by S. Sergeev and the first…

Mathematical Physics · Physics 2013-11-14 Atsuo Kuniba , Masato Okado

We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in $d$ spatial dimensions. The construction provides five boundary charges that are related to certain…

High Energy Physics - Theory · Physics 2017-11-07 Sven Bjarke Gudnason , Zhifeng Gao , Yisong Yang

An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be…

Statistical Mechanics · Physics 2025-09-08 C. Dalitz , E. H. de Groot

We study a bulk-surface coupled Laplace system involving an embedded open boundary. The problem is reformulated as an integro-differential equation using boundary integral representations, for which we establish existence and uniqueness of…

Numerical Analysis · Mathematics 2026-04-23 Charles L. Epstein , Yoichiro Mori , Han Zhou

This paper is concerned with solving the Helmholtz exterior Dirichlet and Neumann problems with large wavenumber $k$ and smooth obstacles using the standard second-kind boundary integral equations. We consider Galerkin and collocation…

Numerical Analysis · Mathematics 2026-03-24 Jeffrey Galkowski , Manas Rachh , Euan A. Spence

We use ring-theoretic methods and methods from the theory of skew braces to produce set-theoretic solutions to the reflection equation. We also use set-theoretic solutions to construct solutions to the parameter-dependent reflection…

Rings and Algebras · Mathematics 2020-01-16 Agata Smoktunowicz , Leandro Vendramin , Robert Weston

This contribution to the Proceedings of the Workshop on Integrable Theories, Solitons and Duality in Sao Paulo in July 2002 summarizes results from the papers hep-th/0112023 and math.QA/0208043. We derive the non-local conserved charges in…

High Energy Physics - Theory · Physics 2007-05-23 Gustav W Delius , Alan George

For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these…

High Energy Physics - Theory · Physics 2009-11-07 G. W. Delius , N. J. MacKay , B. J. Short

This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K,C)-connections on a large class of 3-manifolds M with boundary. We define a space L_K(M) of framed flat connections on the…

High Energy Physics - Theory · Physics 2016-02-03 Tudor Dimofte , Maxime Gabella , Alexander B. Goncharov

In hep-th/9805025, a result for the symmetric 3-loop massive tetrahedron in 3 dimensions was found, using the lattice algorithm PSLQ. Here we give a more general formula, involving 3 distinct masses. A proof is devised, though it cannot be…

High Energy Physics - Theory · Physics 2007-05-23 D. J. Broadhurst

Gapped two-dimensional topological phases can feature ungappable edge states which are robust even in the absence of protecting symmetries. In this work we show that a multipartite entanglement measure recently proposed in the context of…

Quantum Physics · Physics 2022-07-20 Karthik Siva , Yijian Zou , Tomohiro Soejima , Roger S. K. Mong , Michael P. Zaletel

We consider simply connected bodies or regions of finite extent in space or space-time and write conservation laws associated with the equations in Parts I-IV. We review earlier work where, for elliptic equations,the boundary value problem…

Mathematical Physics · Physics 2021-09-24 Graeme W. Milton