87 citations · 582 across the 25 of their papers we have counts for
25 papers
Fermion Families and Pontryagin Class: Topological Field Theory via Colour Symmetry Extension
Zheyan Wan, Juven Wang, Shing-Tung Yau
Family puzzle asks why the Standard Model (SM) features exactly 3 families of quarks and leptons. Motivated by topological constraints, we study 4d fermionic anomalies with discret…
Anomalous (3+1)d Fermionic Topological Quantum Field Theories via Symmetry Extension
Zheyan Wan, Juven Wang
Discrete finite-group global symmetries may suffer from nonperturbative 't-Hooft anomalies. Such global anomalies can be canceled by anomalous symmetry-preserving topological quant…
Anomaly of 4d Weyl fermions with discrete symmetries
Zheyan Wan
We derive explicit anomaly-index formulas for four-dimensional Weyl fermions charged under the finite symmetries Spin and Spin$\times_{\mathbb Z_2^{\mathrm F}}\m…
Topological Responses of the Standard Model Gauge Group
Zheyan Wan, Juven Wang, Yi-Zhuang You
The local Lie algebra of the Standard Model (SM) is , yet its global gauge group, SU(3)SU(2)U(1)/$\mathbb{Z}_{…
C-R-T Fractionalization in the First Quantized Hamiltonian Theory
Yang-Yang Li, Zheyan Wan, Juven Wang +2
Recent research has revealed that the CRT symmetry for fermions exhibits a fractionalization distinct from the $\mathbb{Z}_2^{\mathcal{C}}\times\mathbb{Z}_2^{\mathcal{R}}\times\mat…
A matrix solution to any polygon equation
Zheyan Wan
In this article, we construct matrices associated to Pachner - moves for odd and matrices associated to Pachner - mo…
C-R-T Fractionalization, Fermions, and Mod 8 Periodicity
Zheyan Wan, Juven Wang, Shing-Tung Yau +1
Charge conjugation (C), mirror reflection (R), time reversal (T), and fermion parity are basic discrete spacetime and internal symmetries of the Dirac fermions. In t…
Topological complexity of finding flex points on cubic plane curves
Weiyan Chen, Zheyan Wan
We prove a lower bound for the topological complexity, in the sense of Smale, of the problem of finding a flex point on a cubic plane curve. The key is to bound the Schwarz genus o…
The photography method: solving pentagon equation
Vassily Olegovich Manturov, Zheyan Wan
In the present paper, we consider two applications of the pentagon equation. The first deals with actions of flips on edges of triangulations labelled by rational functions in some…
Proton Stability: From the Standard Model to Beyond Grand Unification
Juven Wang, Zheyan Wan, Yi-Zhuang You
A proton is known for its longevity, but what is its lifetime? While many Grand Unified Theories predict the proton decay with a finite lifetime, we show that the Standard Model (S…
Cobordism and Deformation Class of the Standard Model
Juven Wang, Zheyan Wan, Yi-Zhuang You
't Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a d spacetime are known to be classifie…
3+1d Boundaries with Gravitational Anomaly of 4+1d Invertible Topological Order for Branch-Independent Bosonic Systems
Zheyan Wan, Juven Wang, Xiao-Gang Wen
We study bosonic systems on a spacetime lattice defined by path integrals of commuting fields. We introduce branch-independent bosonic (BIB) systems, whose path integral is indepen…
Studying complex manifolds by using groups and
Vassily Olegovich Manturov, Zheyan Wan
In the present paper, we study several complex manifolds by using the following idea. First, we construct a certain moduli space and study the fundamental group of this space. This…
Extension of elementary -groups and its application in classification of groups of prime exponent
Zheyan Wan, Yu Ye, Chi Zhang
Let be a prime number and . We study finite groups with abelian derived subgroup and exponent in terms of group extension data and thei…
Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew
Zheyan Wan, Juven Wang
We explore QCD quark matter, the -T (chemical potential-temperature) phase diagram, possible 't Hooft anomalies, and topological terms, via non-perturbative tools of cobordi…
Higher Anomalies, Higher Symmetries, and Cobordisms II: Lorentz Symmetry Extension and Enriched Bosonic/Fermionic Quantum Gauge Theory
Zheyan Wan, Juven Wang, Yunqin Zheng
We systematically study Lorentz symmetry extensions in quantum field theories (QFTs) and their 't Hooft anomalies via cobordism. The total symmetry can be expressed in terms o…
Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
Zheyan Wan, Juven Wang
We classify and characterize all invertible anomalies and all allowed topological terms related to various Standard Models (SM), Grand Unified Theories (GUT), and Beyond Standard M…
Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
Zheyan Wan, Juven Wang, Yunqin Zheng
We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-re…
Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
Meng Guo, Kantaro Ohmori, Pavel Putrov +2
We formulate a family of spin Topological Quantum Filed Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf-Witten TQFTs. They are obtained by gauging -equiva…
New Higher Anomalies, SU(N) Yang-Mills Gauge Theory and Sigma Model
Zheyan Wan, Juven Wang, Yunqin Zheng
We hypothesize a new and more complete set of anomalies of certain quantum field theories (QFTs) and then give an eclectic verification. First, we propose a set of 't Hooft higher…
Higher Anomalies, Higher Symmetries, and Cobordisms I: Classification of Higher-Symmetry-Protected Topological States and Their Boundary Fermionic/Bosonic Anomalies via a Generalized Cobordism Theory
Zheyan Wan, Juven Wang
By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in co…
Adjoint QCD, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
Zheyan Wan, Juven Wang
Recent work explores the candidate phases of the 4d adjoint quantum chromodynamics (QCD) with an SU(2) gauge group and two massless adjoint Weyl fermions. Both Cordova-Dumitres…
Classification of spherical fusion categories of Frobenius-Schur exponent 2
Zheyan Wan, Yilong Wang
In this paper, we propose a new approach towards the classification of spherical fusion categories by their Frobenius-Schur exponents. We classify spherical fusion categories of Fr…
Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
Juven Wang, Kantaro Ohmori, Pavel Putrov +6
Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmol…