We present a detailed study of the properties of the phase transition in the four-dimensional compact U(1) lattice gauge theory supplemented by a monopole term, for values of the monopole coupling λ such that the transition is of second order. By a finite size analysis we show that at λ = 0.9 the critical exponent is already characteristic of a second-order transition. Moreover, we find that th...

We review the current status of calculations of the two pion decays of the kaon using the firstprinciples methods of lattice gauge theory and the significant challenges that these calculations pose. While a calculation with controlled errors at even the 10-20% level has not yet been performed, present results suggest that such a calculation of the real and imaginary parts of the ∆I = 3/2 amplit...

We construct a (1,2) heterotic string with gauge symmetry and determine its particle spectrum. This theory has a local N=1 worldsheet supersymmetry for left movers and a local N=2 worldsheet supersymmetry for right movers and describes particles in either two or three space-time dimensions. We show that fermionizing the bosons of the compactified N=1 space leads to a particle spectrum which has...

Suppressing monopoles and vortices by introducing large chemical potentials for them in the Wilson action for the SU(2) lattice gauge theory, we study the nature of the deconfinement phase transition on N σ ×Nτ lattices for Nτ =4, 5, 6 and 8 and Nσ = 8–16. Using finite size scaling theory, we obtain ω ≡ γ/ν = 1.93 ± 0.03 for Nτ = 4, in excellent agreement with universality. The critical couplin...

We construct a variety of supersymmetric gauge theories on a spatial lattice, including N = 4 supersymmetric Yang-Mills theory in 3+1 dimensions. Exact lattice supersymmetry greatly reduces or eliminates the need for fine tuning to arrive at the desired continuum limit in these examples.

If G is any finite product of orthogonal, unitary and symplectic matrix groups, then Wilson loops generate a dense subalgebra of continuous observables on the configuration space of lattice gauge theory with structure group G. If G is orthogonal, unitary or symplectic, then Wilson loops associated to the natural representation of G are enough. This extends a result of A. Sengupta [7]. In partic...

We briefly review an effective theory of QCD at high baryon density, describing the relevant modes near the Fermi surface. The high density effective theory has properties of reparametrization invariance and gauge invariance, maintained in a subtle way. It also has a positive measure, allowing lattice simulations at high baryon density. We then apply it to gapless superconductors and discuss re...

We introduce a new numerical technique to compute mass spectra, based on difference method and on a new gauge fixing procedure. We show that the method is very effective by test runs on a SU(2) lattice gauge theory.

We discuss recent work trying to extract the renormalised quark masses and Λ, the QCD scale, from dynamical simulations in lattice gauge theory.

We review some of the uses of Whitham hierarchies in the context of the theory of the prepotential in N = 2 supersymmetric gauge theories. We focus on the structure of the contact terms in the twisted topological theory, and on the connection between Whitham hierarchies and the u-plane integrals for higher rank gauge groups, trying to put together the different approaches involved in this conne...