The Nielsen-Ninomiya theorem poses an obstacle to constructing discretizations of chiral fermions. However, in two spacetime dimensions bosonization creates a novel loophole. Leveraging recently-proposed modifications of Villain-type lattice actions we can construct lattice regularizations of abelian gauge theory with exact chiral symmetry. The internal global symmetries act just as locally on the lattice as they do in the continuum and the anomalies are correctly reproduced at finite lattice spacing.
I'll give an introduction to the modified Villain formulation, ultimately demonstrating the construction for 2D QED with one and two flavors of Dirac fermions and the `3450' chiral gauge theory. Using exact dualities provides practical algorithms free of sign problems.
Based on work with Aleksey Cherman and Theodore Jacobson, 2310.17539.
Raza Sabbir Sufian, Manu Kurian