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arXiv · 0708.3214

3D N = 1 SYM Chern-Simons theory on the Lattice

Joshua W. Elliott·Guy D. Moore
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Abstract

We present a method to implement 3-dimensional N = 1 SUSY Yang-Mills theory (a theory with two real supercharges containing gauge fields and an adjoint Majorana fermion) on the lattice, including a way to implement the Chern-Simons term present in this theory. At nonzero Chern-Simons number our implementation suffers from a sign problem which will make the numerical effort grow exponentially with volume. We also show that the theory with vanishing Chern-Simons number is anomalous; its partition function identically vanishes.

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Joshua W. Elliott, Guy D. Moore. 2007-11-27. 3D N = 1 SYM Chern-Simons theory on the Lattice. https://doi.org/10.1088/1126-6708%2F2007%2F11%2F067

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