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The fermionic determinant of a lattice Dirac operator that obeys the Ginsparg-Wilson relation factorizes into two factors that are complex conjugate of each other. Each factor is naturally associated with a single chiral fermion and can be realized as a overlap of two many body vacua.

- Robert G. Edwards, Urs M. Heller, Rajamani Narayanan
- Parallel Computing
- 1999

The Overlap-Dirac operator provides a lattice regularization of massless vector gauge theories with an exact chiral symmetry. Practical implementations of this operator and recent results in quenched QCD using this Overlap-Dirac operator are reviewed.

We show that two recent independent proposals for regularizing a chiral gauge theory stem from one common trick. If the anomaly free complex representation carried by the right handed fermi–fields is r one constructs a vector like theory with flavored right handed fermionic matter in r + r̄ but with a mass matrix of the order of the cutoff and having an… (More)

We study three practical implementations of the Overlap-Dirac operator D/ o = 1 2 [1 + γ5ǫ(Hw)] in four dimensions. Two implementations are based on different representations of ǫ(Hw) as a sum over poles. One of them is a polar decomposition and the other is an optimal fit to a ratio of polynomials. The third one is obtained by representing ǫ(Hw) using… (More)

We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character as unitary matrices and undergo a phase transition at infinite N reflected by the eigenvalue distribution closing a gap in its spectrum when the defining smooth… (More)

At infinite N, continuum Euclidean SU N gauge theory defined on a symmetrical four torus has a rich phase structure with phases where the finite volume system behaves as if it had infinite extent in some or all of the directions. In addition, fermions are automatically quenched, so planar QCD should be cheaper to solve numerically that full QCD. Large N is… (More)

In these proceedings, we review some basic properties of the overlap Dirac operator and how its index can be computed by spectral flow techniques. One of the side results is that for fermions in the adjoint representation of SU(N) we find evidence for fractional topological charge. The presentation is pedagogical with the intent of illustrating the origin… (More)

We compute the low lying spectrum of the overlap Dirac operator in the deconfined phase of finite-temperature quenched gauge theory. It suggests the existence of a chiral condensate which we confirm with a direct stochastic estimate. We show that the part of the spectrum responsible for the chiral condensate can be understood as arising from a dilute gas of… (More)

We investigate the approach to the continuum limit of the spectrum of the Hermitian Wilson–Dirac operator in the supercritical mass region for pure gauge SU(2) and SU(3) backgrounds. For this we study the spectral flow of the Hermitian Wilson–Dirac operator in the range 0 ≤ m ≤ 2. We find that the spectrum has a gap for 0 < m ≤ m1 and that the spectral… (More)

The eigenvalue distribution of a Wilson loop operator of fixed shape undergoes a transition under scaling at infinite N . We derive a large N scaling function in a double scaling limit of the average characteristic polynomial associated with the Wilson loop operator in two dimensional QCD. We hypothesize that the transition in three and four dimensional… (More)