Domain wall fermions, anomaly inflow, the ginspargwilson relation. In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Lattice gauge theories are cutoff formulations of gauge theories of strongly interacting particles. Parallels are drawn to abelian lattice gauge theory in four dimensions.
The eigenvalue problem for the hamiltonian of su 2 lattice gauge theory is formulated in the loop representation, which is based on the fact that the physical hilbert space can be spanned by states which are labeled by loops. The three dimensional u1 lattice gauge, in the weak coupling limit, is dual to a discrete gaussian model. Furthermore, using ultracold atoms in optical lattices, an implementation of a lattice gauge theory with a nonabelian gauge group, the dihedral. There is no room for the subtleties associated to the chiral anomaly. We discuss the physics of fourdimensional compact u1 lattice gauge theory from the point of view of softly broken n2 supersymmetric su2 yangmills theory. Since the inner product between loop states can be calculated analytically.
Andrew stromingers 211r course entitled infrared structure of gravity and gauge theory at harvard university. Smith laboratory, department of physics, the ohio state university, 174 w. We investigate this dual model and use it to calculate properties of the u1 theory. Lattice gauge theory for physics beyond the standard model richard c.
Digital quantum simulation of lattice gauge theory energie. Bibliography of edward witten school of natural sciences. This chapter is an introduction to the main concepts of lattice gauge theory. The lattice formulation is designed to enable such computations the lattice formulation is the only known formulation which contains perturbative and nonperturbative \sectors. Lattice gauge theories an introduction theoretisch. This is a project aimed at constructing gaugeinvariant tensor networks for lattice gauge theory with a view to obtaining a continuous groundstate ansatz for pure yangmills theory. Large gauge symmetry in nonabelian gauge theory lecture 6 of 10.
Gauge theories are important in particle physics, and include the prevailing theories of elementary particles. Gauge fields, the wilson action, the haar measure, the strong coupling expansion. Lattice gauge theory is a regulated version of quantum. Neil,2, simon catterall,3 george fleming,4 joel giedt,5 enrico rinaldi,6, 7 david schaich,8, 9 evan weinberg,1, 10 and oliver witzel2 usqcd collaboration 1 department of physics and center for computational science, boston university. Statistical mechanics and field theory are closely related subjects. Lattice gauge theory for physics beyond the standard model. This means that we are back in the realm of quantum mechanics. An introduction to lattice gauge theory and spin systems physical. Bibliography of edward witten 1 heavy quark contributions to deep inelastic scattering, nucl. Pdf an introduction to lattice gauge theory researchgate.
Pdf lattice gauge theory for physics beyond the standard. Pdf an introduction to lattice gauge theory and spin systems. It is therefore to be regarded as the formulation definition of a quantum field theory, in particular qcd. Although a number of impressive mathematical advances have occurred over the years 14,23,25,2729,36,4042,45, 50,53,54,59,6365, no lattice gauge theory in any dimension higher than two has been rigorously solved in the above sense. Lattice gauge theories naturally explain confinement in the strong coupling limit.
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