I review some of the contributions which lattice simulations are likely to make during the next five years or so to the development of our understanding of particle physics. Particular emphasis is given to the evaluation of non-perturbative QCD effects in experimentally measurable amplitudes, and the corresponding extraction of fundamental parameters.

Recent progress in the field of lattice gauge theories is briefly reviewed for a nonspecialist audience. While the emphasis is on the latest and more definitive results that have emerged prior to this symposium, an effort has been made to provide them with minimal technicalities.

Title of dissertation: TOPICS IN LATTICE QCD AND EFFECTIVE FIELD THEORY Michael I. Buchoff, Doctor of Philosophy, 2010 Dissertation directed by: Associate Professor Paulo Bedaque Department of Physics Quantum Chromodynamics (QCD) is the fundamental theory that governs hadronic physics. However, due to its non-perturbative nature at low-energy/long distances, QCD calculations are difficult. The ...

Supersymmetric gauge theories have had a significant impact on our understanding of QCD and of field theory in general. The phases of N = 1 supersymmetric QCD (SQCD) are discussed, and the possibility of similar phases in non-supersymmetric QCD is emphasized. It is described how duality in SQCD links many previously known duality transformations that were thought to be distinct, including Olive...

The classical superconformal actions of branes in adS superspaces have a closed form depending on a matrix M quadratic in fermions, as found in hep-th/9805217. One can gauge-fix the local κ-symmetry using the Killing spinors of the brane in the bulk. We show that in such gauges the superconformal actions are simplified dramatically since M = 0 in all cases. The relation between classical and ga...

For this after dinner talk I intersperse images of real lattices with a discussion of the motivations for lattice gauge theory and some current unresolved issues.

We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix geometries. The approximation is carried out for both irrational and rational deformation parameters by embedding the C∗-algebra of the noncommutative torus into an approximately finite algebra. The construction is a rigorous derivation of the recent discretizations of non...

We consider recently-constructed solutions of three dimensional SL(N,R)×SL(N,R) Chern-Simons theories with non-relativistic symmetries. Solutions of the Chern-Simons theories can generically be mapped to solutions of a gravitational theory with a higherspin gauge symmetry. However, we will show that some of the non-relativistic solutions are not equivalent to metric solutions, as this mapping f...

We propose a large N dual of 4d, N = 1 supersymmetric, SU(N) Yang-Mills with adjoint field Φ and arbitrary superpotential W (Φ). The field theory is geometrically engineered via D-branes partially wrapped over certain cycles of a non-trivial Calabi-Yau geometry. The large N , or low-energy, dual arises from a geometric transition of the Calabi-Yau, where the branes have disappeared and have bee...

Bosonic string formation in gauge theories is reviewed with particular attention to the confining flux in lattice QCD and its string theory description. Recent results on the Casimir energy of the ground state and the string excitation spectrum are analyzed in the Dirichlet string limit of large separation between static sources. The closed string-soliton (torelon) with electric flux winding ar...