Twisted supersymmetries in lattice $\mathcal{N}=4$ super Yang-Mills theory

Abstract

Recently it has been shown how a topologically twisted version of $\mathcal{N}=4$ super Yang-Mills may be discretized in such a way as to preserve one scalar supersymmetry at nonzero lattice spacing. The remaining fifteen supersymmetries are broken by terms of $\mathcal{O}(a)$ where $a$ is the lattice spacing. One would like to know whether these remaining supersymmetries are regained in the continuum limit $a\to 0$ and, if not, how much tuning of the couplings in the lattice action is required. In this paper we derive the form of these additional twisted supersymmetries by combining a set of discrete R-symmetries of the continuum theory with the action of the scalar supersymmetry. We then argue that restoration of rotational symmetry in the continuum limit of the lattice theory likely implies restoration of R-symmetry and hence should lead to an automatic enhancement to the full $\mathcal{N}=4$ supersymmetry without further fine-tuning.

v3: Published version

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• Real space renormalization group for twisted lattice N=4 super Yang-Mills
• Progress and prospects of lattice supersymmetry
• Supersymmetry on the lattice
• Lifting flat directions in lattice supersymmetry
• Three-dimensional super-Yang--Mills theory on the lattice and dual black branes
• Lattice formulation of three-dimensional $\mathcal{N}=4$ gauge theory with fundamental matter fields
• Lattice studies of supersymmetric gauge theories
• Two-dimensional $\mathcal{N}=(2,2)$ Lattice Gauge Theories with Matter in Higher Representations
• Supersymmetric quiver gauge theories on the lattice
• Lattice N=4 super Yang-Mills at Strong Coupling
• 3d N=4 Super-Yang-Mills on a Lattice
• A Euclidean Lattice Formulation of D=5 Maximally Supersymmetric Yang-Mills Theory
• Eigenvalue spectrum of lattice $\mathcal{N}=4$ super Yang-Mills
• Eigenvalue spectrum and scaling dimension of lattice $\mathcal{N}=4$ supersymmetric Yang-Mills
• Lattice Formulation of $\mathcal{N}=2^{\ast }$ Yang-Mills
• A one-loop test for construction of 4D N=4 SYM from 2D SYM via fuzzy sphere geometry
• Spontaneous supersymmetry breaking in two dimensional lattice super QCD
• Two dimensional super QCD on a lattice
• Nonperturbative phase diagram of two-dimensional $\mathcal{N}=(2,2)$ super-Yang--Mills
• $\mathcal{N}=2^{\ast }$ Yang-Mills on the Lattice