Detecting Standard Model Gauge Group from Generalized Fractional Quantum Hall Effect

We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled to an emergent Chern-Simons gauge field. These gapless quasiparticles can be understood as composites of electrons and Laughlin-like quasiparticles. We show that semi-quantized quantum Hall states exhibit perfect interlayer drag, host non-...

Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian ...

We discuss heavy particles that can be used to pin down the faithful Standard Model (SM) gauge group and their patterns in the SM effective field theory (SMEFT). These heavy particles are not invariant under a specific $\mathbb{Z}_6$ subgroup of $SU(3)_c\times SU(2)_L \times U(1)_Y$, which however acts trivially on all the SM particles, hence the faithful SM gauge group remains undetermined. Different realizations of the faithful SM gauge group correspond to different spectra...

We study the Standard Model with gauged $\mathbb Z_{N=2,3,6}^{(1)}$ subgroups of its $\mathbb Z_6^{(1)}$ 1-form global symmetry, making the gauge group $SU(3) \times SU(2)\times U(1) \over \mathbb Z_N$. We show that, on a finite $\mathbb T^3$, there are self-dual instantons of fractional topological charge. They mediate baryon- and lepton-number violating processes. We compare their amplitudes to the ones due to the usual BPST-instantons. We find that the small hypercharge co...

This article is based on the talk "Fractional Spin Gravity" presented in the 31st International Colloquium on Group Theoretical Methods in Physics, Rio de Janeiro, 19-25th June 2016. There we emphasised an implication of the works [1,2] by N. Boulanger, P. Sundell and the author on fractional spin extensions of 2+1D higher spin gravity. This is that higher spin gravity may govern interactions of pseudo-particles excitations in the (fractional) quantum Hall effect. More genera...

We present a general algebraic framework for gauging a 0-form compact, connected Lie group symmetry in (2+1)d topological phases. Starting from a symmetry fractionalization pattern of the Lie group $G$, we first extend $G$ to a larger symmetry group $\tilde{G}$, such that there is no fractionalization with respect to $\tilde{G}$ in the topological phase, and the effect of gauging $\tilde{G}$ is to tensor the original theory with a $\tilde{G}$ Chern-Simons theory. To restore t...

Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to address fundamental dynamical questions. I survey recent work in this area.

We develop a systematic theory of symmetry fractionalization for fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group $G_f$. In general $G_f$ is a central extension of the bosonic symmetry group $G_b$ by fermion parity, $(-1)^F$, characterized by a non-trivial cohomology class $[\omega_2] \in \mathcal{H}^2(G_b, \mathbb{Z}_2)$. We show how the presence of local fermions places a number of constraints on the algebraic data that defines the ac...

We study $N$-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU$(N)$-invariant interactions based on density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU$(N)$ fractional quantum Hall states can emerge at fractional filling factors $\nu=N/(N+1)$ for bosons ($\nu=N/(2N+1)$ for fermions) in the lowest Chern band, characterized ...

We consider topological invariants describing semimetal (gapless) and insulating (gapped) states of the quantum vacuum of Standard Model and possible quantum phase transitions between these states.