We demonstrate that Maxwell electrodynamics interacting with a planar Chern-Simons interface does not have plane wave solutions localized on the interface. We re-examine the derivation of such waves presented by N. Kaloper in [Phys.Rev.D114(2026)L051903] and show that at an intermediate step certain terms were missed in an equation therein. Taking these terms into account changes the final conclusion of [Phys.Rev.D114(2026)L051903]. We also show that the method used in [arXiv:2606.12513 [hep-th]] to reproduce the same result is not consistent.
Tunable surface plasmons on the interface of a multilevel atomic medium with a cross coupling of the electric and magnetic components of a plasmonic field are investigated. The strong chirality resulting from the quantum coherence leads to some exciting properties of the surface plasmons. Compared to the traditional chiral-metal interface, surface plasmonic mode can still be found at the interface between such atomic media and a dielectric even when both the permittivity and the permeability of the medium are positive. This is in contrast to the conventional plasmonic systems where the signs of the permittivities or permeabilities on the two sides of the interface are opposite. We call this phenomenon an electromagnetically induced plasmon. Additionally, as the chirality and effective refractive index of the atomic medium are dependent on the intensity and phase of the controlling field, we can conveniently manipulate the properties of the surface plasmons.
Hints of cosmic microwave background polarization rotation (
Δϑ∼10−3 rad) are commonly attributed to late-time dynamics of ultralight axions. We show that such ultralight degrees of freedom are not required. Polarization rotation naturally arises as a geometric interface phase acquired when photons cross interfaces between topologically distinct dark sector vacua. The effect is a discrete phase shift fixed by the normalization of a wall-supported electromagnetic Chern--Simons interaction and protected by an emergent
1-form symmetry of the low energy effective theory. This mechanism reproduces the familiar adiabatic rotation induced by light axion domain walls, but persists for arbitrarily thin walls where the axion is heavy or absent. In this regime the rotation manifests as a Pancharatnam phase localized at vacuum interfaces, independent of redshift and photon frequency below a natural ultraviolet cutoff. Cosmic birefringence thus emerges as a probe of vacuum structure in the dark sector, rather than of light-field dynamics.
Framing anomaly is a key property of
(2+1)d chiral topological orders, for it reveals that the chirality is an intrinsic bulk property of the system, rather than a property of the boundary between two systems. Understanding framing anomaly in lattice models is particularly interesting, as concrete, solvable lattice models of chiral topological orders are rare. In a recent work, we defined and solved the
U(1) Chern-Simons-Maxwell theory on spacetime lattice, showing its chiral edge mode and the associated gravitational anomaly on boundary. In this work, we show its framing anomaly in the absence of boundary, by computing the expectation of a lattice version of the modular
T operator in the ground subspace on a spatial torus, from which we extract that
⟨T⟩ has a universal phase of
−2π/12 as expected:
−2π/8 from the Gauss-Milgram sum of the topological spins of the ground states, and
2π/24 from the framing anomaly; we can also extract the
2π/24 framing anomaly phase alone from the full spectrum of
T in the ground subspace by computing
⟨Tm⟩. This pins down the last and most crucial property required for a valid lattice definition of
U(1) Chern-Simons theory.
Maxwell-Chern-Simons (MCS) theory in
2+1 dimensions provides a paradigmatic example of a topological gauge theory with both dynamical and topological degrees of freedom. Its Euclidean formulation suffers from a sign problem, making Hamiltonian numerical approaches particularly attractive. As a first step toward the non-perturbative Hamiltonian study of MCS theory, we investigate the constant mode sector on a spatial torus. Being analytically solvable in the continuum, it provides an ideal benchmark for understanding how the topological properties of the theory are encoded in a finite-dimensional lattice Hilbert space. We construct a finite-dimensional discretization of the torus of flat connections and show that the resulting lattice problem maps onto a generalized Harper-Hofstadter model with twisted boundary conditions. We identify the commensurability conditions under which the finite lattice exactly reproduces the magnetic translation algebra and the topological degeneracy of the continuum theory. A systematic analysis of gauge field truncation and its convergence toward the continuum limit is then presented.
Abstract The low energy effective field theories of (2 + 1) dimensional topological phases of matter provide powerful avenues for investigating entanglement in their ground states. In [1] the entanglement between distinct Abelian topological phases was investigated through Abelian Chern-Simons theories equipped with a set of topological boundary conditions (TBCs). In the present paper we extend the notion of a TBC to non-Abelian Chern-Simons theories, providing an effective description for a class of gapped interfaces across non-Abelian topological phases. These boundary conditions furnish a defining relation for the extended Hilbert space of the quantum theory and allow the calculation of entanglement directly in the gauge theory. Because we allow for trivial interfaces, this includes a generic construction of the extended Hilbert space in any (compact) Chern-Simons theory quantized on a Riemann surface. Additionally, this provides a constructive and principled definition for the Hilbert space of effective ground states of gapped phases of matter glued along gapped interfaces. Lastly, we describe a generalized notion of surgery, adding a powerful tool from topological field theory to the gapped interface toolbox.