Detecting Standard Model Gauge Group from Generalized Fractional Quantum Hall Effect

Built upon the previous work on the 4d anomalies and 5d cobordism invariants (namely, 5d invertible field theory [iTFT] or symmetry-protected topological state [SPTs]) of the Standard Model [SM] gauge theory with compatible (SU(3)$\times$SU(2)$\times$U(1))/$\mathbb{Z}_q$ gauge group for $q=1,2,3,6$, we further enumerate lower-dimensional iTFT / SPTs in 4d, 3d, 2d, and 1d. While the 4d SPTs are interesting gapped phases attachable to the SM, those integer classes of SPTs (eith...

The gauge group of strong and electroweak interactions in Nature could be any of the four that share the same Lie algebra, $SU(3)_c\times SU(2)_L\times U(1)_Y/Z_p\equiv G_p$ with $Z_p=\left\{Z_6,Z_3,Z_2,Z_1\right\}$. Each of these cases allows in its spectrum for the matter fields of the SM but also for new distinctive representations, e.g. under the assumption that $q_L$ possesses the minimum possible hypercharge in Nature, $G_p$ allows for particles with a multiple of $p\,e...

The observed Standard Model is consistent with the existence of vector-like species with electric charge a multiple of $e/6$. The discovery of a fractionally charged particle would provide nonperturbative information about Standard Model physics, and furthermore rule out some or all of the minimal theories of unification. We discuss the phenomenology of such particles and focus particularly on current LHC constraints, for which we reinterpret various searches to bound a varie...

The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter $\theta$. $\theta = 0, \pi$ correspond to bosons and fermions respectively; at intermediate values we say that we have fractional statistics. In two dimensions, $\theta$ describes the phase...

Fractional quantum Hall (FQH) states are examples of symmetry-enriched topological states (SETs): in addition to the intrinsic topological order, which is robust to symmetry breaking, they possess symmetry-protected topological invariants, such as fractional charge of anyons and fractional Hall conductivity. In this paper we develop a comprehensive theory of symmetry-protected topological invariants for FQH states with spatial symmetries, which applies to Abelian and non-Abel...

$U(n\otimes m)\ast$ gauge field theory on noncommutative spacetime is formulated and the standard-like model with the symmetry ${\text{U}(3_c\otimes 2\otimes 1_{\text{\scriptsize$Y$}})\ast}$ is reconstructed based on it. $\text{U}(n+m)\ast$ gauge group reduces to $\text{U}(n+m)$ on the commutative spacetime which is not ${\text{U}}(N), (N=n+m)$ but isomorphic to $\text{SU}(n)\times\text{SU}(m)\times \text{U}(1)$ in this article. On the noncommutative spacetime, the representa...

We investigate fractionalization of non-invertible symmetry in (2+1)D topological orders. We focus on coset non-invertible symmetries obtained by gauging non-normal subgroups of invertible $0$-form symmetries. These symmetries can arise as global symmetries in quantum spin liquids, given by the quotient of the projective symmetry group by a non-normal subgroup as invariant gauge group. We point out that such coset non-invertible symmetries in topological orders can exhibit sy...

The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined "anyons", may exist. The fractiona...

One of the most intriguing aspects of Chern-Simons-type topological models is the fractional statistics of point particles which has been shown essential for our understanding of the fractional quantum Hall effects. Furthermore these ideas are applied to the study of high Tc superconductivity. We present here an recently proposed model for fractional spin with the Pauli term. On the other hand, in D=4 space-time, a Schwarz-type topological gauge theory with antisymmetric tens...

We construct a class of 2+1 dimensional relativistic quantum field theories which exhibit the Fractional Quantum Hall Effect in the infrared, both in the continuum and on the lattice. The UV completion consists of a perturbative $U(1)\times U(1)$ gauge theory with only integer-charged fields, while the low energy spectrum consists of nontrivial topological phases supporting fractional currents, fractionally charged chiral surface modes and bulk anyonic excitations. Exotic phe...