Deconstruction, 2d lattice Yang-Mills, and the dynamical lattice spacing

Abstract

We study expectation values related to the dynamical lattice spacing that occurs in the recent supersymmetric 2d lattice Yang-Mills constructions of Cohen et al. [hep-lat/0307012]. For the purposes of this preliminary analysis, we restrict our attention to the bosonic part of that theory. That is, we compute observables in the fully quenched ensemble, equivalent to non-supersymmetric 2d lattice Yang-Mills with a dynamical lattice spacing and adjoint scalars. Our numerical simulations indicate difficulties with the proposed continuum limit. We find that expectation values tend to those of the undeformed ``daughter theory,'' in spite of the deformation suggested by Cohen et al. In an effort to understand these results, we examine the zero action configurations, with and without the deformation. Based on these considerations, we are able to interpret the simulation results in terms of entropic effects.

arXiv comment1+16 pages, 2 figures, minor improvements to discussion

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• Lattice supersymmetry, superfields and renormalization
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• Simulations of $\mathcal{N}=2$ super Yang-Mills theory in two dimensions
• Progress in four-dimensional lattice supersymmetry
• Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice
• Compact Gauge Fields for Supersymmetric Lattices
• Perturbative Study of the Supersymmetric Lattice Theory from Matrix Model
• R-symmetry in the Q-exact (2,2) 2d lattice Wess-Zumino model
• N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one exact supersymmetry
• A local formulation of lattice Wess-Zumino model with exact $\U(1)_R$ symmetry
• Lattice formulation of 2D $\mathcal{N}=(2,2)$ SQCD based on the B model twist
• Advances and applications of lattice supersymmetry
• A deconstruction lattice description of the D1/D5 brane world-volume gauge theory