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The bulk-edge correspondence (BEC) is the hallmark of topological systems. In continuous (nonlattice) Hermitian systems with an unbounded wave vector, it was recently shown that the BEC of Chern insulators is modified. How would it be…

Mesoscale and Nanoscale Physics · Physics 2023-02-13 Orr Rapoport , Moshe Goldstein

The abelian Chern-Simons theory is considered on a cylindrical spacetime $\mathbb{R} \times D$, in a not necessarily flat Lorentzian background. As in the flat bulk case with planar boundary, we find that also on the radial boundary of a…

High Energy Physics - Theory · Physics 2021-11-15 Erica Bertolini , Giulio Gambuti , Nicola Maggiore

Topological invariants, such as the winding number, the Chern number, and the Zak phase, characterize the topological phases of bulk materials. Through the bulk-boundary correspondence, these topological phases have a one-to-one…

Disordered Systems and Neural Networks · Physics 2025-10-24 R. Moola , A. Mckenna , M. Hilke

We consider the two-point functions of conserved bulk currents and energy-momentum tensor in a boundary CFT defined on $\mathbb{R}_-^{1,2}$. Starting from the consistent forms of boundary gauge and gravitational anomalies we derive their…

High Energy Physics - Theory · Physics 2019-07-11 Vladimir Prochazka

An explicit, detailed evaluation of the classical continuum limit of the axial anomaly/index density of the overlap Dirac operator is carried out in the infinite volume setting, and in a certain finite volume setting where the continuum…

High Energy Physics - Lattice · Physics 2009-10-31 David H. Adams

We investigate abelian Chern-Simons gauge theory on a strip geometry with two spatial boundaries. In the presence of boundaries, gauge invariance is broken by boundary conditions, leading to physical edge excitations. By deriving the most…

High Energy Physics - Theory · Physics 2026-04-29 Erica Bertolini , Michael Doyle , Nicola Maggiore , Conor Murphy , Carlotta Piras

Recently, general methods of bosonization beyond 1+1 dimensions have been developed. In this article, we review these bosonizations and extend them to the case with boundary conditions. In particular, we study the case when the bulk theory…

Strongly Correlated Electrons · Physics 2019-07-18 Ryan Thorngren

Chiral and non-chiral $p$-form gauge fields have gravitational anomalies and anomalies of Green-Schwarz type. This means that they are most naturally realized as the boundary modes of bulk topological phases in one higher dimensions. We…

High Energy Physics - Theory · Physics 2025-12-05 Chang-Tse Hsieh , Yuji Tachikawa , Kazuya Yonekura

In the background of a charged AdS black hole, we consider a Dirac particle endowed with an arbitrary magnetic dipole moment. For non-zero charge and dipole coupling of the bulk fermion, we find that the dual boundary theory can be plagued…

High Energy Physics - Theory · Physics 2016-01-27 Manuela Kulaxizi , Rakibur Rahman

Some aspects of the theory of fermions living on three dimensional spacetime with a flat co-dimension one boundary are discussed, particularly a case where the boundary condition preserves scale and translation invariance but violates the…

High Energy Physics - Theory · Physics 2024-03-21 Gordon W. Semenoff

Bulk-edge correspondence is a wide-ranging principle that applies to topological matter, as well as a precise result established in a large and growing number of cases. According to the principle, the distinctive topological properties of…

Mathematical Physics · Physics 2025-05-12 Gian Michele Graf , Alessandro Tarantola

We consider a Dirac operator with constant magnetic field defined on a half-plane with boundary conditions that interpolate between infinite mass and zigzag. By a detailed study of the energy dispersion curves we show that the infinite mass…

Mathematical Physics · Physics 2024-01-24 Loïc Le Treust , Jean-Marie Barbaroux , Horia D. Cornean , Edgardo Stockmeyer , Nicolas Raymond

Bulk-edge correspondence is a cornerstone in topological physics, establishing a connection between the number of unidirectional edge modes in physical space and a Chern number, an integer that counts phase singularities of the eigenmodes…

Other Condensed Matter · Physics 2024-06-17 Yohei Onuki , Antoine Venaille , Pierre Delplace

We study anomalies of six-dimensional gauge theories compactified on orbifolds. In addition to the known bulk anomalies, brane anomalies appear on orbifold fixpoints in the case of chiral boundary conditions. At a fixpoint, where the bulk…

High Energy Physics - Phenomenology · Physics 2010-11-19 T. Asaka , W. Buchmüller , L. Covi

In a class of systems, there are gapped boundary-localized states described by a boundary Hamiltonian. The topological classification of gapped boundary Hamiltonians, same as the standard tenfold way for gapped bulk states, can lead to the…

Mesoscale and Nanoscale Physics · Physics 2025-06-23 Xun-Jiang Luo , Fengcheng Wu

We study bulk/edge aspects of continuous honeycomb lattices in a magnetic field. We compute the bulk index of Bloch eigenbundles: it equals $2$ or $-2$, with sign depending on nearby Dirac points and on the magnetic field. We then prove the…

Analysis of PDEs · Mathematics 2019-01-21 Alexis Drouot

As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The…

Mesoscale and Nanoscale Physics · Physics 2023-08-01 Kazuki Sone , Motohiko Ezawa , Yuto Ashida , Nobuyuki Yoshioka , Takahiro Sagawa

This paper concerns the topological classification of continuous Hamiltonians that find applications in biased cold plasmas and photonics. Besides a magnetic bias, the Hamiltonians are parametrized by a plasma frequency and a fixed vertical…

Mathematical Physics · Physics 2026-04-20 Matthew Frazier , Guillaume Bal

Boundary conditions for a massless Dirac fermion in 2+1 dimensions where the space is a half-plane are discussed in detail. It is argued that linear boundary conditions that leave the Hamiltonian Hermitian generically break $C$ $P$ and $T$…

High Energy Physics - Theory · Physics 2022-10-26 Shovon Biswas , Gordon W. Semenoff

We study topological aspects of defect modes for a family of operators $\{\mathscr{P}(t)\}_{t \in [0,2\pi]}$ on $L^2(\mathbb{R})$. $\mathscr{P}(t)$ is a periodic Schr\"odinger operator $P_0$ perturbed by a dislocated potential. This…

Analysis of PDEs · Mathematics 2019-01-30 Alexis Drouot