literature
Literature
Authors
Jobs
Seminars
Conferences
DataBETA

Noncommutative chiral anomaly and the Dirac-Ginsparg-Wilson operator

Nov, 2002
21 pages
Published in:
  • JHEP 08 (2003) 046
e-Print:
DOI:
Report number:
  • SU-4252-747,
  • DIAS-02-12
View in:
pdf
reference search29 citations

Citations per year

200320082013201820213710
Abstract: (arXiv)
It is shown that the local axial anomaly in 2−2-dimensions emerges naturally if one postulates an underlying noncommutative fuzzy structure of spacetime . In particular the Dirac-Ginsparg-Wilson relation on SF2{\bf S}^2_F is shown to contain an edge effect which corresponds precisely to the ``fuzzy'' U(1)AU(1)_A axial anomaly on the fuzzy sphere . We also derive a novel gauge-covariant expansion of the quark propagator in the form 1DAF=aΓ^L2+1DAa\frac{1}{{\cal D}_{AF}}=\frac{a\hat{\Gamma}^L}{2}+\frac{1}{{\cal D}_{Aa}} where a=22l+1a=\frac{2}{2l+1} is the lattice spacing on SF2{\bf S}^2_F, Γ^L\hat{\Gamma}^L is the covariant noncommutative chirality and DAa{\cal D}_{Aa} is an effective Dirac operator which has essentially the same IR spectrum as DAF{\cal D}_{AF} but differes from it on the UV modes. Most remarkably is the fact that both operators share the same limit and thus the above covariant expansion is not available in the continuum theory . The first bit in this expansion aΓ^L2\frac{a\hat{\Gamma}^L}{2} although it vanishes as it stands in the continuum limit, its contribution to the anomaly is exactly the canonical theta term. The contribution of the propagator 1DAa\frac{1}{{\cal D}_{Aa}} is on the other hand equal to the toplogical Chern-Simons action which in two dimensions vanishes identically .
Note:
  • 26 pages, latex file
  • gauge field theory: U(1)
  • gauge field theory: action
  • space-time: noncommutative
  • anomaly: chiral
  • sphere: fuzzy
  • Ginsparg-Wilson relation
  • fermion: chiral
  • invariance: gauge
  • operator: Dirac
  • matrix model
  • 1-25 of 35
  • 1
  • 2
  • 25 / page