Related papers: Spinons and parafermions in fermion cosets
Known symmetry groups are insufficient to describe the various couplings among spin, charge, and spatial degrees of freedom in fermionic systems. To address this problem, we introduce spin-charge groups (SCGs), which provide a unified…
We analyse the SU(2)_k WZNW models beyond the integrable representations and in particular the case of SU(2)_0. We find that these are good examples of logarithmic conformal field theories as indecomposable representations are naturally…
$\mathcal{N}=1$ superconformal minimal models are the first series of unitary conformal field theories (CFTs) extending beyond Virasoro algebra. Using coset constructions, we characterize CFTs in $\mathcal{N}=1$ superconformal minimal…
In this article we outline the historical development and key results obtained to date for free parafermionic spin chains. The concept of free parafermions provides a natural N-state generalization of free fermions, which have long…
We construct Narain conformal field theories (CFTs) from quantum subsystem codes, a more comprehensive class of quantum error-correcting codes than quantum stabilizer codes, for qudit systems of prime dimensions. The resulting code CFTs…
In a recent paper, we developed and applied a dilaton-based effective field theory (EFT) to the analysis of lattice-simulation data for a class of confining gauge theories with near-conformal infrared behavior. It was employed there at the…
A new parafermionic algebra associated with the homogeneous space $A^{(2)}_2/U(1)$ and its corresponding $Z$-algebra have been recently proposed. In this paper, we give a free boson representation of the $A^{(2)}_2$ parafermion algebra in…
We consider several gauge invariant higher dimensional operators that couple gravity, gauge fields and scalar or fermionic fields and thus break conformal invariance. In particular, we consider terms that break conformal invariance by the…
We study the properties of 2+1d conformal field theories (CFTs) in a background magnetic field. Using generalized particle-vortex duality, we argue that in many cases of interest the theory becomes gapped, which allows us to make a number…
We introduce prepotentials for fermionic higher-spin gauge fields in four spacetime dimensions, generalizing earlier work on bosonic fields. To that end, we first develop tools for handling conformal fermionic higher-spin gauge fields in…
We prove the equivalence of VOA tensor categories and conformal net tensor categories for the following examples: all WZW models; all lattice VOAs; all unitary parafermion VOAs; type $ADE$ discrete series $W$-algebras; their tensor…
I give an elementary introduction to the study of gauge theories coupled to fermions with many degrees of freedom. Besides their intrinsic interest, these theories are candidates for nonperturbative extensions of the Higgs sector of the…
We employ the $\mathrm{SU}(n)_k$ Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions. The spins on all lattice sites are chosen to transform under the $\mathrm{SU}(n)$…
We define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups $\Gamma_\vartheta$, $\Gamma^0(2)$ and $\Gamma_0(2)$ of $\text{SL}_2(\mathbb Z)$. Each subgroup corresponds to one of the spin structures on the…
We suggest model equations, which, from some point of view, describe local interaction of three physical fields: a field of matter, an electromagnetic field and a gravitational field. A base of the model is a field of matter described by…
We describe the dynamics of a single fermion in a dispersionless band coupled to the 2+1 dimensional conformal field theory (CFT) describing the quantum phase transition of a bosonic order parameter with N components. The fermionic spectral…
We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin TQFTs at low energy. We formulate a $16$-fold way conjecture for…
We propose a connection between conformal field theory (CFT) and the exact solution and integrability of the reduced BCS model of superconductivity. The relevant CFT is given by the $SU(2)_k$-WZW model in the singular limit when the level k…
We develop a partial charge-spin separation fermion-spin theory implemented the gauge invariant dressed holon and spinon. In this novel approach, the physical electron is decoupled as the gauge invariant dressed holon and spinon, with the…
One of the major frontiers of lattice field theory is the inclusion of light fermions in simulations, particularly in pursuit of accurate, first principles predictions from lattice QCD. With dedicated Teraflops-scale computers currently…