Supersymmetric Yang--Mills theories with exact supersymmetry on the lattice

Abstract

Inspired by the ideas from topological field theory it is possible to rewrite the supersymmetric charges of certain classes of extended supersymmetric Yang--Mills (SYM) theories in such a way that they are compatible with the discretization on a Euclidean spacetime lattice. Such theories are known as maximally twisted SYM theories. In this review we discuss the construction and some applications of such classes of theories. The one-loop perturbative renormalization of the four-dimensional lattice $\mathcal{N}=4$ SYM is discussed in particular. The lattice theories constructed using twisted approach play an important role in investigating the thermal phases of strongly coupled SYM theories and also the thermodynamic properties of their dual gravitational theories.

74 pages, 15 figures, minor revision, references added, published version

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Cited by in corpus (20)

• Phase Structure of Lattice N=4 Super Yang-Mills
• Twisted supersymmetries in lattice $\mathcal{N}=4$ super Yang-Mills theory
• On the sign problem in 2D lattice super Yang--Mills
• Direct test of the AdS/CFT correspondence by Monte Carlo studies of N=4 super Yang-Mills theory
• Review of Lattice Supersymmetry and Gauge-Gravity Duality
• Lattice formulation of three-dimensional $\mathcal{N}=4$ gauge theory with fundamental matter fields
• An object oriented code for simulating supersymmetric Yang--Mills theories
• Lattice formulation of two-dimensional N=(2,2) super Yang-Mills with SU(N) gauge group
• Supersymmetric quiver gauge theories on the lattice
• Two-dimensional $\mathcal{N}=(2,2)$ Lattice Gauge Theories with Matter in Higher Representations
• Improved lattice actions for supersymmetric quantum mechanics
• Supersymmetric Gauge Theory on the Graph
• Mass spectrum of $2$-dimensional $\mathcal{N}=(2,2)$ super Yang-Mills theory on the lattice
• A Euclidean Lattice Formulation of D=5 Maximally Supersymmetric Yang-Mills Theory
• Two-dimensional $\mathcal{N}=2$ Super-Yang-Mills Theory
• An anisotropic hybrid non-perturbative formulation for 4D N = 2 supersymmetric Yang-Mills theories
• Lattice Formulation of $\mathcal{N}=2^{\ast }$ Yang-Mills
• 2D discrete Yang-Mills equations on the torus
• $\mathcal{N}=2^{\ast }$ Yang-Mills on the Lattice
• Grand Pleromal Transmutation : condensates via Konsishi anomaly, dimensional transmutation and ultraminimal GUTs