From Domain Wall to Overlap in 2+1d

Abstract

The equivalence of domain wall and overlap fermion formulations is demonstrated for lattice gauge theories in 2+1 spacetime dimensions with parity-invariant mass terms. Even though the domain wall approach distinguishes propagation along a third direction with projectors $\frac{1}{2}(1\pm {\gamma }_3)$, the truncated overlap operator obtained for finite wall separation $L_s$ is invariant under interchange of ${\gamma }_3$ and ${\gamma }_5$. In the limit $L_s\to \infty$ the resulting Ginsparg-Wilson relations recover the expected U($2N_f$) global symmetry up to O($a$) corrections. Finally it is shown that finite-$L_s$ corrections to bilinear condensates associated with dynamical mass generation are characterised by whether even powers of the symmetry-breaking mass are present; such terms are absent for antihermitian bilinears such as $i\bar{\psi }{\gamma }_3\psi$, markedly improving the approach to the large-$L_s$ limit.

13 pages

References in corpus (7)

• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Massive fermions without fermion bilinear condensates
• Critical behavior of the (2+1)-dimensional Thirring model
• Critical Flavor Number in the Three Dimensional Thirring Model
• Fermion mass without symmetry breaking
• Critical flavour number of the Thirring model in three dimensions
• Critical flavour number of the Thirring model in three dimensions

Cited by in corpus (12)

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• Critical Behaviour in the Single Flavor Thirring Model in 2+1d
• Scale-invariance and scale-breaking in parity-invariant three-dimensional QCD
• Spectroscopy in the 2+1$d$ Thirring Model with $N=1$ Domain Wall Fermions
• A curious behavior of three-dimensional lattice Dirac operators coupled to monopole background
• Critical Behaviour in the Single Flavor Thirring Model in 2+1$d$ with Wilson Kernel Domain Wall Fermions
• Transition in the spectral gap of the massless overlap Dirac operator coupled to abelian fields in three dimensions
• Evaluation of the Bilinear Condensate of the Planar Thirring Model in the Strongly Coupled Region
• Lattice Field Theory Analysis of the Chiral Heisenberg Model