Nonperturbative numerical analysis of SY M(1+1)
I. Filippov · OhioLink ETD Center (Ohio Library and Information Network) · 2002
Recent string theory developments suggest the necessity to understand supersymmetric gauge theories non- perturbatively, in various dimensions. Some of the advantages of using SDLCQ—that is, Supersymmetric Discrete Light Cone Quantization, when one deals with supercharge instead of the hamiltionian are better convergence and absence of singularities. In this work we show that there is a standard Hamiltonian formulation that generates a finite and supersymmetric result at every order of the DLCQ approximation scheme. We present this DLCQ renormalized Hamiltonian and solve for the bound states and the wave functions to verify that it exactly reproduces the large Nc SDLCQ results. To extend the advantages of SDLCQ to non-supersymmetric theories we consider supersymmetry breaking of the 1 + 1 dimension N = (1,1) SYM theory that is obtained by dimensionally reducing SYM theory in 2 + 1 dimensions to 1 + 1 dimension. The field content of this theory is an adjoint boson and an adjoint fermion. We discuss the numerical simulation of this theory using SDLCQ when either the boson or the fermion has a larger mass. We compare our result for the pure adjoint fermion theory and the pure adjoint boson DLCQ calculation with those of Klebanov, Demeterfi and Bhanot and of Kutasov.