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Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
Xiao-Gang Wen
The usual condensed matter lattice theories do not include dynamical electromagnetic (EM) field and do not have higher symmetries naturally (unless we engineer fine-tuned toy model…
A New SU(2) Anomaly
Juven Wang, Xiao-Gang Wen, Edward Witten
A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more gene…
Fermion decoration construction of symmetry protected trivial orders for fermion systems with any symmetries and in any dimensions
Tian Lan, Chenchang Zhu, Xiao-Gang Wen
We use higher dimensional bosonization and fermion decoration to construct exactly soluble interacting fermion models to realize fermionic symmetry protected trivial (SPT) orders (…
A Non-Perturbative Definition of the Standard Models
Juven Wang, Xiao-Gang Wen
The Standard Models contain chiral fermions coupled to gauge theories. It has been a long-standing problem to give such gauged chiral fermion theories a quantum non-perturbative de…
A continuous topological phase transition between two 1D anti-ferromagnetic spin-1 boson superfluids with the same symmetry
Wenjie Ji, Xiao-Gang Wen
Spin-1 bosons on a 1-dimensional chain, at incommensurate filling with anti-ferromagnetic spin interaction between neighboring bosons, may form a spin-1 boson condensed state that…
Topological non-linear -model, higher gauge theory, and a realization of all 3+1D topological orders for boson systems
Chenchang Zhu, Tian Lan, Xiao-Gang Wen
A discrete non-linear -model is obtained by triangulate both the space-time and the target space . If the path integral is given by the sum of all the complex homom…