Related papers: General corner charge formulas in various tetrahed…
Constructing charges in the covariant phase space formalism often leads to formally divergent expressions, even when the fields satisfy physically acceptable fall-off conditions. These expressions can be rendered finite by corner…
In gravitational theories with boundaries, diffeomorphisms can become physical and acquire a non-vanishing Noether charge. Using the covariant phase space formalism, on shell of the gravitational constraints, the latter localizes on…
It is shown that the physical ``quark number'' charges which appear in the central charge of the supersymmetry algebra of $N=2$ supersymmetric QCD can take irrational values and depend non trivially on the Higgs expectation value. This…
Conserved charges in theories with gauge symmetries are supported on codimension-2 surfaces in the bulk spacetime. It has recently been suggested that various classical formulations of gravity dynamics display different symmetries, and…
I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields…
The modern theory of polarization allows for the determination of the macroscopic end charge of a truncated one-dimensional insulator, modulo the charge quantum $e$, from a knowledge of bulk properties alone. A more subtle problem is the…
Conformally invariant functionals on the space of knots are introduced via extrinsic conformal geometry of the knot and integral geometry on the space of spheres. Our functionals are expressed in terms of a complex-valued 2-form which can…
In this second paper of the series we continue to spell out a new program for quantum gravity, grounded in the notion of corner symmetry algebra and its representations. Here we focus on tetrad gravity and its corner symplectic potential.…
The spatial charge arrangement of a typical quasi-two-dimensional organic conductor alpha-(BEDT-TTF)2I3 is revealed by single crystal structure analysis using synchrotron radiation. The results show that the horizontal stripe type…
F-theory, as a 12-dimensional theory that is a contender of the Theory of Everything, should be compactified into elliptically fibered threefolds or fourfolds of Calabi-Yau. Such manifolds have an elliptic curve as a fiber, and their bases…
We show that topological defects in quadrupole insulators do not host quantized fractional charges, contrary to what their Wannier representation indicates. In particular, we test the charge quantization hypothesis based on the Wannier…
In the previous works, it was claimed that black holes can be considered as topological insulators. In this paper, we will show that they are actually fractional topological insulators. That is, the quasi-particles and quasi-holes can have…
We discuss some bulk-surfaces gapped Hamiltonians on a lattice with corners and propose a periodic table for topological invariants related to corner states aimed at studies of higher-order topological insulators. Our table is based on four…
In quantum chromodynamics with static quarks the confinement-deconfinement phase transition is connected to the spontaneous breaking of the global Z3 center symmetry. This symmetry is lost when one considers dynamical quarks. Owing to the…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
We study K-theoretic GLSM invariants with one-dimensional gauge group and introduce elliptic central charges that depend on an elliptic cohomology class called an elliptic brane and a choice of level structure. These central charges have an…
Topological materials are renowned for their ability to harbor states localized at their peripheries, such as surfaces, edges, and corners. Accompanying these states, fractional charges appear on peripheral unit cells. Recently,…
This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different…
The effective fractional charges like 17/4 or 19/4 are explained by our angular momentum theory. These fractions do not arise from the odd denominator rule. Due to spin polarization for both of these along the magnetic field, these states…
Following recent works on corner charges we investigate the boundary structure in the case of the theory of gravity formulated as a constrained BF theory. This allows us not only to introduce the cosmological constant, but also explore the…