Related papers: $\mathbb{Z}_3$ Parafermionic Chain Emerging From Y…
Generalized Z_k^(r/2) parafermionic theories - characterized by the dimension (r/2)(1-1/k) of the basic parafermionic field - provide potentially interesting quantum-Hall trial wavefunctions. Such wavefunctions reveal a W_k structure. This…
We propose an adjoint $SU(5)$ GUT model with a $T_{7}$ family symmetry and an extra $Z_{2}\otimes Z_{3}\otimes Z_{4}\otimes Z_{4}^{\prime }\otimes Z_{12}$ discrete group, that successfully describes the prevailing Standard Model fermion…
Using $\mathbb{Z}_3$ symmetry, we present a topological condition for the existence of the $\mathbb{Z}_2$ harmonic 1-forms over Riemannian manifold. As a corollary, if $L$ is an oriented link on $S^3$ with determinant zero, then there…
We consider the heterotic string on Calabi-Yau manifolds admitting a Strominger-Yau-Zaslow fibration. Upon reducing the system in the $T^3$-directions, the Hermitian Yang-Mills conditions can then be reinterpreted as a complex flat…
Parafermions, which can be viewed as a fractionalized version of Majorana modes, exhibit profound non-Abelian statistics and emerge in topologically ordered systems, while their realization in experiment has been challenging. Here we…
The framed standard model (FSM) suggested earlier, which incorporates the Higgs field and 3 fermion generations as part of the framed gauge theory structure, is here developed further to show that it gives both quarks and leptons…
A new family of non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation is constructed. All these solutions are strong twisted unions of multipermutation solutions of multipermutation level at most two. A large…
We present a model which contains three Abelian symmetries beyond the standard model. One is anomalous {\it \` a la} Green-Schwarz, and family-independent; the other two are family symmetries. All are broken at a large scale by stringy…
A review of orbifold geometry is given, followed by a review of the construction of four-dimensional heterotic string models by compactification on a six-dimensional Z_3 orbifold. Particular attention is given to the details of the…
We present the first multiscalar singlet extension of the 3-3-1 model with right-handed neutrinos, based on the $\Delta \left( 27\right) $ family symmetry, supplemented by the $Z_{4}\otimes Z_{8}\otimes Z_{14}$ flavor group, consistent with…
We study $\mathbb{Z}_3$ symmetry-protected topological (SPT) phases in one-dimensional spin systems with $Z_3 \times Z_3$ symmetry. We construct ground-state wave functions of the matrix product form for nontrivial $\mathbb{Z}_3$ phases and…
The SYK model proposed by Sachdev, Ye, and Kitaev consists of Majorana fermions that interact randomly four at a time. The model develops a dense spectrum above the ground state, due to which the model becomes nearly conformal. This…
The graded parafermion conformal field theory at level k is a close cousin of the much-studied Z_k parafermion model. Three character formulas for the graded parafermion theory are presented, one bosonic, one fermionic (both previously…
We present a systematic analysis of a minimal supersymmetric $Z_3$ discrete flavor symmetry as a solution to the fermion mass hierarchy problem. With generation-dependent $Z_3$ charges on the right-handed chiral superfields and a single…
Spin-charge separation in pure SU(2) Yang-Mills theory was recently found to involve the dynamics of an O(3) non-linear sigma model and, seemingly, a Grassmannian non-linear sigma model. In this article we explicitly construct the…
We discuss a new SU(3)_C X SU(3)_L X U(1)_X X U(1)_N (3-3-1-1) gauge model that overhauls the theoretical and phenomenological aspects of the known 3-3-1 models. Additionally, we sift the outcome of the 3-3-1-1 model from precise…
We prove that abelian Yang-Baxter deformations of superstring coset sigma models are equivalent to sequences of commuting TsT transformations, meaning T dualities and coordinate shifts. Our results extend also to fermionic deformations and…
Building on previous work, we extend an algebraic realisation of three fermion generations within the complex Clifford algebra $\mathbb{C}\ell(8)$ by incorporating a $U(1)_{em}$ gauge symmetry. The algebra $\mathbb{C}\ell(8)$ corresponds to…
Multifold fermions, quasiparticles with multiple degeneracy protected by crystalline symmetries, exhibit a variety of intriguing phenomena stemming from their large topological charges and unique band structures. A comprehensive…
We study the spin-$1$ Babujian-Takhtajan chain deformed by its third conserved charge $Q_3$. We derive $Q_3$ and show that it is a dimensionless energy current and that its local density is a dressed scalar-chirality operator rather than…