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- Simon Catterall
- 2004

We propose a discretization of two dimensional Euclidean Yang-Mills theories with N = 2 supersymmetry which preserves exactly both gauge invariance and an element of supersymmetry. The approach starts from the twisted form of the continuum super Yang Mills action which we show may be written in terms of two real Kähler-Dirac fields whose components… (More)

- Simon Catterall
- 2003

We discuss the connection between supersymmetric field theories and topological field theories and show how this connection may be used to construct local lattice field theories which maintain an exact supersymmetry. It is shown how metric independence of the continuum topological field theory allows us to derive the lattice theory by blocking out of the… (More)

- Simon Catterall
- 2001

Starting from a simple discrete model which exhibits a supersymmetric invariance we construct a local, interacting, two-dimensional Euclidean lattice theory which also admits an exact supersymmetry. This model is shown to correspond to the Wess-Zumino model with extended N = 2 supersymmetry in the continuum. We have performed dynamical fermion simulations… (More)

We show that lattice regularization of noncommutative field theories can be used to study non-perturbative vacuum phases. Specifically we provide evidence for the existence of a striped phase in two-dimensional noncommutative scalar field theory.

- Simon Catterall
- 2005

We construct a lattice action for N = 4 super Yang-Mills theory in four dimensions which is local, gauge invariant, free of spectrum doubling and possesses a single exact supersymmetry. Our construction starts from the observation that the fermions of the continuum theory can be mapped into the component fields of a single real anticommuting Kähler-Dirac… (More)

- Simon Catterall
- 2006

We present results from lattice simulations of N = 2 super Yang-Mills theory in two dimensions. The lattice formulation we use was developed in [1] and retains both gauge invariance and an exact (twisted) supersymmetry for any lattice spacing. Results for both U(2) and SU(2) gauge groups are given. We focus on supersymmetric Ward identities, the phase of… (More)

- Simon Catterall
- 1994

We present the results of a high statistics Monte Carlo study of a model for four dimensional euclidean quantum gravity based on summing over triangulations. We show evidence for two phases; in one there is a logarithmic scaling of the mean linear extent with volume, whilst the other exhibits power law behaviour with exponent 1 2 . We are able to extract a… (More)

- Simon Catterall
- 1998

We show that the phase transition previously observed in dynamical triangulation models of quantum gravity can be understood as being due to the creation of a singular link. The transition between singular and non-singular geometries as the gravitational coupling is varied appears to be first order. Dynamical triangulations (DT) furnish a powerful approach… (More)

By a sequence of numerical experiments we demonstrate that generic triangulations of the D−sphere forD > 3 contain one singular (D−3)−simplex. The mean number of elementary D−simplices sharing this simplex increases with the volume of the triangulation according to a simple power law. The lower dimension subsimplices associated with this (D − 3)−simplex… (More)