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Following Symanzik we argue that the Schrödinger functional in lattice gauge theories without matter fields has a well-defined continuum limit. Due to gauge invariance no extra counter terms are required. The Schrödinger functional is, moreover, accessible to numerical simulations. It may hence be used to study the scaling properties of the theory and in… (More)

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.

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)

- R. Narayanan, H. Neuberger
- 2006

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)

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)

- R. Narayanan, H. Neuberger
- 2008

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)

- R. Narayanan, H. Neuberger
- 2008

It is established by numerical means that continuum large N QCD defined on a three dimensional torus can exist in four different phases. They are (i) confined phase; (ii) deconfined phase; (iii) small box at zero temperature and (iv) small box at high temperatures.

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 define a sparse hermitian lattice Dirac matrix, H, coupling 2n+ 1 Dirac fermions. When 2n fermions are integrated out the induced action for the last fermion is a rational approximation to the hermitian overlap Dirac operator. We provide rigorous bounds on the condition number of H and compare them to bounds for the higher dimensional Dirac operator of… (More)