N=(1,1) super-Yang–Mills on a (2+1)-dimensional transverse lattice with one exact supersymmetry

Abstract

We formulate N =1 super Yang-Mills theory in 3+1 dimensions on a two dimensional transverse lattice using supersymmetric discrete light cone quantization in the large-N c limit. This formulation is free of fermion species doubling. We are able to preserve one supersymmetry. We find a rich, non-trivial behavior of the mass spectrum as a function of the coupling g √ N c , and see some sort of "transition" in the structure of a bound state as we go from the weak coupling to the strong coupling. Using a toy model we give an interpretation of the rich behavior of the mass spectrum. We present the mass spectrum as a function of the winding number for those states whose color flux winds all the way around in one of the transverse directions. We use two fits to the mass spectrum and the one that has a string theory justification appears preferable. For those states whose color flux is localized we present an extrapolated value for m 2 for some low energy bound states in the limit where the numerical resolution goes to infinity.

Deconstruction and Other Approaches to Supersymmetric Lattice Field Theories

“…This allows for more symmetry to be preserved (associated with the light-cone), and reduces the dimensionality of the lattice system that must be simulated. An example of this type of construction is [92].…”

Solution to the fermion doubling problem for supersymmetric theories on the transverse lattice

“…To focus on the fermion species doubling problem of the transverse lattice [3], let us consider fermion fields only by setting the coupling g = 0 and the link variables M, M † = 1. For this theory one spatial dimension is discretized on a spatial lattice.…”

“…In Ref. [3] we proposed a discrete transverse lattice formulation of the supercharge Q − , which gives the correct continuum form and the P − obtained from SUSY algebra {Q − , Q − } = 2 √ 2P − also gives the correct continuum form. With this P − in hand, following the same procedure we did in the previous section, we set g = 0 and M, M † = 1 to see whether we suffer from the fermion doubling problem.…”

“…Recently, the authors proposed a super Yang-Mills (SYM) model in 2+1 dimensions on a transverse lattice with one exact supersymmetry [3]. It is well known that in the standard Lagrangian formulation of SYM on the transverse lattice one finds a fermion species doubling problem.…”

Ginsparg-Wilson Formulation of 2D N = (2,2) SQCD with Exact Lattice Supersymmetry

“…Lattice formulations for supersymmetric field theories, which preserve a part of their supersymmetry, have been constructed -in [1,2,3,4] for two-dimensional Wess-Zumino models or sigma models without gauge symmetry, in [5,6,7,8,9,10,11,12,13,14,15] for pure super Yang-Mills (SYM) theories, and in [16,17,18] for two-dimensional SYM theories coupled with matter multiplets 1 . For the remaining supercharges, which are broken by the latticization, ref.…”