Talks by Juven Wang
String and particle excitations are examined in a class of 3+1D topological order described by a discrete gauge theory with a gauge group G and a 4-cocycle twist ω4∈H4(G,R/Z) of G's cohomology group. We demonstrate the topological spin and the spin-statistics relation for the closed strings, and their multi-string braiding. The 3+1D twisted gauge theory can be characterized by a representation of SL(3,Z) modular transformation, which we find its generators Sxyz and Txy in terms of the gauge group G and the 4-cocycle ω4.
A non-perturbative definition of anomaly-free chiral fermions and bosons in 1+1D spacetime as finite quantum systems on 1D lattice is proposed. In particular, any 1+1D anomaly-free chiral matter theory can be defined as finite quantum systems on 1D lattice with on-site symmetry, if we include strong interactions between matter fields. Our approach provides another way, apart from Ginsparg-Wilson fermions approach, to avoid the fermion-doubling challenge.