2014/07/13 by El Hassan Saidi, Saidi, El Hassan
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #hep-lat #hep-th
paper · pdf · doi:10.48550/arxiv.1407.3854
LaTex, 81 pages, 4 figures
arxiv created 2014/07/13 · arxiv updated 2014/07/16
We study a class of twisted 3D N=4 supersymmetric Yang-Mills (SYM) theory on particular 3-dimensional lattice denoted as L3Dsu3× u1 and given by non trivial fibration L1Du1× L2Dsu3 with base L2Dsu3=\mathbbA2^∗, the weight lattice of SU(3). We first, develop the twisted 3D N=4 SYM in continuum by using superspace method where the scalar supercharge Q is manifestly exhibited. Then, we show how to engineer the 3D lattice L3Dsu3× u1 that host this theory. After that we build the lattice action Slatt invariant under the 3 following: (i) U(N) gauge invariance, (ii) BRST symmetry, (iii) the hidden SU(3) × U(1) symmetry of L3Dsu3× u1. Other features such as reduction to twisted 2D supersymmetry with 8 supercharges living on L2Dsu2× u1, the extension to twisted maximal 5D SYM with 16 supercharges on lattice L5Dsu4× u1 as well as the relation with known results are also given.