Twisted 3D $N=4$ Supersymmetric YM on deformed $\mathbb{A}_3^\ast$ Lattice

El Hassan Saidi

paper

Twisted 3D $N = 4$ Supersymmetric YM on deformed $A_{3}^{*}$ Lattice

arXiv:1407.3854

Abstract

We study a class of twisted 3D $N = 4$ supersymmetric Yang-Mills (SYM) theory on particular 3-dimensional lattice denoted as $L_{3 D}^{s u_{3} \times u_{1}}$ and given by non trivial fibration $L_{1 D}^{u_{1}} \times L_{2 D}^{s u_{3}}$ with base $L_{2 D}^{s u_{3}} = A_{2}^{*}$ , the weight lattice of $S U (3)$ . 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 $L_{3 D}^{s u_{3} \times u_{1}}$ that host this theory. After that we build the lattice action $S_{l a tt}$ invariant under the 3 following: (i) $U (N)$ gauge invariance, (ii) BRST symmetry, (iii) the hidden $S U (3) \times U (1)$ symmetry of $L_{3 D}^{s u_{3} \times u_{1}}$ . Other features such as reduction to twisted 2D supersymmetry with 8 supercharges living on $L_{2 D}^{s u_{2} \times u_{1}}$ , the extension to twisted maximal 5D SYM with 16 supercharges on lattice $L_{5 D}^{s u_{4} \times u_{1}}$ as well as the relation with known results are also given.

LaTex, 81 pages, 4 figures

Twisted 3D N=4 Supersymmetric YM on deformed A3∗​ Lattice

Abstract

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Twisted 3D $N = 4$ Supersymmetric YM on deformed $A_{3}^{*}$ Lattice