The Status of D-Theory

Field theories are usually quantized by performing a path integral over configurations of classical fields. This is the case both in perturbation theory and in Wilson's nonperturbative lattice field theory. D-theory is an alternative nonperturbative formulation of field theory in which classical fields emerge from the low-energy collective dynamics of discrete quantum variables (quantum spins and their gauge analogs -- quantum links) which undergo dimensional reduction. D-theory was developed some time ago as a discrete approach to U(1) and SU(2) pure gauge theories, extended to SU(N) gauge theories and full QCD, and also applied to a variety of other models. On the practical side, D-theory provides a framework for the development of efficient numerical methods, such as cluster algorithms. For example, in the D-theory formulation of CP(N-1) models one can simulate efficiently at non-zero chemical potential or at non-zero vacuum angle theta. On the conceptual side, D-theory offers a natural solution for the nonperturbative hierarchy problem of chiral symmetry in QCD. We also take a broader nonperturbative view on fundamental physics and speculate that D-theory variables -- i.e. quantum spins and quantum links -- may be promising candidates for the physical degrees of freedom that Nature has chosen to regularize the standard model physics at ultra-short distances.