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SUMMARY:Quantized axial charge of staggered fermions and the chiral anomal
 y - Arkya Chatterjee\, MIT
DTSTART:20241128T141500Z
DTEND:20241128T151500Z
UID:TALK225127@talks.cam.ac.uk
CONTACT:Laurens Lootens
DESCRIPTION:Realizing chiral global symmetries on a finite lattice is a lo
 ng-standing challenge in lattice gauge theory\, with potential implication
 s for non-perturbative regularization of the Standard Model. One of the si
 mplest examples of such a symmetry is the axial U(1) symmetry of the 1+1d 
 massless Dirac fermion field theory: it acts by equal and opposite phase r
 otations on the left- and right-moving Weyl components of the Dirac field.
  This field theory also has a vector U(1) symmetry which acts identically 
 on left- and right-movers. The two U(1) symmetries exhibit a mixed anomaly
 \, known as the chiral anomaly. In this talk\, we will discuss how both sy
 mmetries are realized as ordinary U(1) symmetries of an ``ultra-local" lat
 tice Hamiltonian\, on a finite-dimensional Hilbert space. Intriguingly\, t
 he anomaly of the Abelian U(1) symmetries in the infrared (IR) field theor
 y is matched on the lattice by a non-Abelian Lie algebra. The lattice symm
 etry forces the low-energy phase to be gapless\, closely paralleling the e
 ffects of the anomaly in the field theory.
LOCATION:MR2
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