Nonperturbative solution of supersymmetric gauge theories

Recent work on the numerical solution of supersymmetric gauge theories is described. The method used is SDLCQ (supersymmetric discrete light-cone quantization). An application to N=1 supersymmetric Yang-Mills theory in 2+1 dimensions at large N_c is summarized. The addition of a Chern-Simons term is also discussed.Comment: 9 pages, LaTeX2e, ws-procs9x6; to appear in the proceedings of the fifth workshop on Continuous Advances in QCD (Arkadyfest), Minneapolis, Minnesota, May 17-23, 200

Pauli-Villars regularization in DLCQ

Calculations in a (3+1)-dimensional model indicate that Pauli-Villars regularization can be combined with discrete light-cone quantization (DLCQ) to solve at least some field theories nonperturbatively. Discrete momentum states of Pauli-Villars particles are included in the Fock basis to automatically generate needed counterterms; the resultant increase in basis size is found acceptable. The Lanczos algorithm is used to extract the lowest massive eigenstate and eigenvalue of the light-cone Hamiltonian, with basis sizes ranging up to 10.5 million. Each Fock-sector wave function is computed in this way, and from these one can obtain values for various quantities, such as average multiplicities and average momenta of constituents, structure functions, and a form-factor slope.Comment: 6 pages, 1 figure; LaTeX, aiproc.sty, epsf.sty; to appear in the proceedings of the Eleventh International Light-Cone Workshop on New Directions in QCD, Kyungju, Korea, June 20-25, 199

Pauli-Villars regularization of field theories on the light front

Four-dimensional quantum field theories generally require regularization to be well defined. This can be done in various ways, but here we focus on Pauli--Villars (PV) regularization and apply it to nonperturbative calculations of bound states. The philosophy is to introduce enough PV fields to the Lagrangian to regulate the theory perturbatively, including preservation of symmetries, and assume that this is sufficient for the nonperturbative case. The numerical methods usually necessary for nonperturbative bound-state problems are then applied to a finite theory that has the original symmetries. The bound-state problem is formulated as a mass eigenvalue problem in terms of the light-front Hamiltonian. Applications to quantum electrodynamics are discussed.Comment: 8 pages, PoS.cls; to appear in the proceedings of Light Cone 2010, Valencia, Spain, June 14-18, 201

A nonperturbative coupled-cluster method for quantum field theories

The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from many-body coupled-cluster theory, to obtain form factors and other observables.Comment: 4 pages; presented at CIPANP 2012, the Eleventh Conference on the Intersections of Particle and Nuclear Physics, May 28 - June 3, 2012, St. Petersburg, Florid

Pauli-Villars regularization and discrete light-cone quantization in Yukawa theory

The techniques of Pauli-Villars regularization and discrete light-cone quantization are combined to analyze Yukawa theory in a single-fermion truncation. A special form of the Lanczos algorithm is constructed for diagonalization of the indefinite-metric light-cone Hamiltonian.Comment: 6 pages; LaTeX, sprocl.sty; to appear in the proceedings of the CSSM Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, Adelaide, Australia, December 13-21, 199