Related papers: Edge States in 4D and their 3D Groups and Fields
Continuum grid-like frames composed of rigidly jointed beams are classic subjects in the field of structural mechanics, whose topological dynamical properties have only recently been revealed. For two-dimensional frames, higher-order…
This is intended as a broad introduction to Chern-Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant system --with a fiber bundle formulation-- in more than three dimensions,…
In 2025, Bernardes, Erler and Firat proposed a novel, elegant expression for the symplectic form on phase space applicable to non-local theories. We show that this BEF symplectic structure can be derived directly from an…
We study effectively one-dimensional systems that emerge at the edge of a two-dimensional topologically ordered state, or at the boundary between two topologically ordered states. We argue that anyons of the bulk are associated with…
We consider Chern-Simons theory on 3-manifold $M$ that is the total space of a circle bundle over a 2d base $\Sigma$. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained…
We use the 3d-3d correspondence together with the DGG construction of theories $T_n[M]$ labelled by 3-manifolds M to define a non-perturbative state-integral model for SL(n,C) Chern-Simons theory at any level k, based on ideal…
In these lectures I review classical aspects of the self-dual Chern-Simons systems which describe charged scalar fields in $2+1$ dimensions coupled to a gauge field whose dynamics is provided by a pure Chern-Simons Lagrangian. These…
The spin 1 bilinear-biquadratic model on square lattice in the region $0<\phi<\pi/4$ is studied in a fermion representation with a p-wave pairing BCS type mean-field theory. Our results show there may exist a non-trivial gapped spin liquid…
Starting from a recently proposed linear formulation in terms of auxiliary fields, we study $n$-field generalizations of Born and Born-Infeld theories. In this description the Lagrangian is quadratic in the vector field strengths and the…
We study an exotic state which is localized only at an intersection of edges of a topological material. This "edge-of-edge" state is shown to exist generically. We construct explicitly generic edge-of-edge states in 5-dimensional Weyl…
A Lagrangian description of a maximally supersymmetric conformal field theory in three dimensions was constructed recently by Bagger and Lambert (BL). The BL theory has SO(4) gauge symmetry and contains scalar and spinor fields that…
A Lagrangian multiform structure is established for a generalisation of the Darboux system describing orthogonal curvilinear coordinate systems. It has been shown in the past that this system of coupled PDEs is in fact an encoding of the…
The $(D+1)$-dimensional symmetry topological field theory (SymTFT$_{D+1}$) of a $D$-dimensional absolute quantum field theory (QFT$_D$) provides a topological characterization of symmetry data. In this framework, the SymTFT comes equipped…
The Maxwell-Chern-Simons (MCS) Lagrangian is the Maxwell Lagrangian augmented by the Chern-Simons (CS) term. In this paper, we study the MCS and Maxwell Lagrangians on a disk $D$. They are of interest for the quantum Hall effect, and also…
A regular lattice of magnetic skyrmions is the ground state of thin ferromagnetic films with Dzyaloshinskii-Moriya interaction in a relatively wide range of external magnetic fields. It was previously theoretically shown that upon the…
The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a…
The bulk-edge correspondence in topological phases is extended to systems with the generalized chiral symmetry, where the conventional chiral symmetry is broken. In such systems, we find that the edge state exhibits an unconventional…
We show that edge states similar to those known for topological insulators exist in two-dimensional electron system with one-band spectrum in the presence of heterogeneous spin-orbit interaction (SOI). These states appear at boundaries…
We introduce the self-dual abelian gauged $O(3)$ sigma models where the Maxwell and Chern-Simons terms constitute the kinetic terms for the gauge field. These models have quite rich structures and various limits. Our models are found to…
A direct relation between two types of topological field theories, Chern-Simons theory and BF theory, is presented by using ``Generalized Differential Calculus'', which extends an ordinary p-form to an ordered pair of p and (p+1)-form. We…