PIRSA:13120069 Scientific Series Condensed Matter

DOI10.48660/13120069

Series: Quantum Matter

Wang, J. (2013). A lattice non-perturbative definition of chiral fermion/gauge theory from Topological Order . Perimeter Institute. https://pirsa.org/13120069

Wang, Juven. A lattice non-perturbative definition of chiral fermion/gauge theory from Topological Order . Perimeter Institute, Dec. 13, 2013, https://pirsa.org/13120069 

@misc{ pirsa_PIRSA:13120069,
  doi = {10.48660/13120069},
  url = {https://pirsa.org/13120069},
  author = {Wang, Juven},
  keywords = {Condensed Matter},
  language = {en},
  title = {A lattice non-perturbative definition of chiral fermion/gauge theory from Topological Order },
  publisher = {Perimeter Institute},
  year = {2013},
  month = {dec},
  note = {PIRSA:13120069 see, \url{https://pirsa.org}}
}

Abstract

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. In general, using the defining connection between gauge anomalies and the symmetry-protected topological orders, we propose that any truly anomaly-free chiral gauge theory can be non-perturbatively defined by putting it on a lattice in the same dimension. As an additional remark, we conjecture/prove the equivalence relation between 't Hooft anomaly matching conditions and the boundary fully gapping rules.

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